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In the statistical physics of disordered systems, the random energy model is a toy model of a system with quenched disorder, such as a spin glass, having
Random_energy_model
Disordered magnetic state
similar meanings as in the EA model. The p → ∞ {\displaystyle p\to \infty } limit of this model is known as the random energy model. In this limit, the probability
Spin_glass
Model in statistical mechanics
large-k limit. This is similar to how the random energy model is the large-p limit of the p-spin glass model. There are N {\displaystyle N} particles.
Random_subcube_model
Two-dimensional conformal field theory
c\geq 25} , and certain log-correlated random energy models. These models describe a thermal particle in a random potential that is logarithmically correlated
Liouville_field_theory
Set of random variables
appropriate (locally defined) energy function. The prototypical Markov random field is the Ising model; indeed, the Markov random field was introduced as the
Markov_random_field
Mathematical model of ferromagnetism in statistical mechanics
The Ising model (or Lenz–Ising model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical
Ising_model
French theoretical physicist
Weisbuch, G (1986-08-01). "Evolution of overlaps between configurations in random Boolean networks" (PDF). Journal de Physique. 47 (8): 1297–1303. doi:10
Bernard_Derrida
French mathematician
topics including Hopfield networks, the long-term behavior of the random energy model and similar glassy systems, and metastability in reversible diffusion
Véronique_Gayrard
Model in physical chemistry
The energy difference also introduces a non-randomness at the local molecular level. The NRTL model belongs to the so-called local-composition models. Other
Non-random_two-liquid_model
Statistical tool to model changing systems
In probability theory, a Markov model is a stochastic model used to model pseudo-randomly changing systems. It is assumed that future states depend only
Markov_model
French physicist and academic administrator
In 2001, he joined the Center for Theoretical Physics and Statistical Models at the University of Paris-Sud, and he serves as its director. Since 2012
Marc_Mézard
British theoretical physicist
Sherrington–Kirkpatrick model, to systems with p-spin interactions and defined, together with Bernard Derrida, the Generalized Random Energy Model (GREM). When working
Elizabeth_Gardner_(physicist)
Statistical method
Random sample consensus (RANSAC) is an iterative method to estimate parameters of a mathematical model from a set of observed data that contains outliers
Random_sample_consensus
Mathematical limit applied in statistical physics
systems. The random energy model (REM) is one of the simplest models of statistical mechanics of disordered systems, and probably the simplest model to show
Replica_trick
French mathematician (born 1957)
Bovier, Anton; Gayrard, Véronique (2003). "Glauber Dynamics of the Random Energy Model" (PDF). Communications in Mathematical Physics. 236 (1): 1–54. Bibcode:2003CMaPh
Gérard_Ben_Arous
Class of statistical modeling methods
pattern recognition and machine learning, conditional random field (CRF) is a class of statistical modeling methods often used for structured prediction. Unlike
Conditional_random_field
Polymer conformation in which all bonded subunits are oriented randomly
value. Also, many polymers have random branching. Even with corrections for local constraints, the random walk model ignores steric interference between
Random_coil
Matrix-valued random variable
that the nuclear Hamiltonian could be modeled as a random matrix. For larger atoms, the distribution of the energy eigenvalues of the Hamiltonian could
Random_matrix
Random motion of particles suspended in a fluid
models. There exist sequences of both simpler and more complicated stochastic processes which converge (in the limit) to Brownian motion (see random walk
Brownian_motion
Field of physics that studies polymers
of a random walk, the self-avoiding walk. The simplest possible polymer model is presented by the ideal chain, corresponding to a simple random walk.
Polymer_physics
Engineering model
models, with tree-based models and Gaussian process models built in. Surrogates.jl is a Julia packages which offers tools like random forests, radial basis
Surrogate_model
Economic model showing fair trading leads to inequality
yard-sale model, also known as the yard sale effect, is a kinetic exchange market model in which agents repeatedly exchange wealth in random pairs, with
Yard-sale_model
Cosmological models involving indefinite, self-sustaining cycles
more recent cyclic model of 2007 assumes an exotic form of dark energy called phantom energy, which possesses negative kinetic energy and would usually
Cyclic_model
Type of stochastic recurrent neural network
change of sign in the energy function) are found in Paul Smolensky's "Harmony Theory". Ising models can be generalized to Markov random fields, which find
Boltzmann_machine
Branch of mathematics in probability theory
as well as the study of random graphs and random geometric graphs. Continuum percolation arose from an early mathematical model for wireless networks,
Continuum_percolation_theory
Model in statistical mechanics generalizing the Ising model
Random cluster model Critical three-state Potts model Chiral Potts model Square-lattice Ising model Minimal models Z N model Cellular Potts model Wu
Potts_model
Technique for the generative modeling of a continuous probability distribution
original dataset. A diffusion model models data as generated by a diffusion process, whereby a new datum performs a random walk with drift through the space
Diffusion_model
Hypothesis in neuroscience
for embodied perception-action loops in neuroscience. The free energy principle models the behaviour of one system that is distinct from, but coupled
Free_energy_principle
Physical theory of the cosmos
directions in the sky and the shape of the energy versus intensity curve, both consistent with the Big Bang models of high temperatures and densities in the
Big_Bang
Probability distribution
distribution. A random variable which is log-normally distributed takes only positive real values. It is a convenient and useful model for measurements
Log-normal_distribution
Type of machine learning model
A large language model (LLM) is an AI model (typically a neural network) trained on a vast amount of text for natural language processing tasks, especially
Large_language_model
Physical quantity
is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces. Energy transformations in the universe
Energy
Computational model of cells and tissues
minimizes this energy. In order to evolve the model Metropolis-style updates are performed, that is: choose a random lattice site i choose a random neighboring
Cellular_Potts_model
Probabilistic problem-solving algorithm
optimization, numerical integration, and non-uniform random variate generation, available for modeling phenomena with significant input uncertainties, e
Monte_Carlo_method
Maximum-entropy random graph models are random graph models used to study complex networks subject to the principle of maximum entropy under a set of
Maximum-entropy random graph model
Maximum-entropy_random_graph_model
Statistical tool used in meta-analyses
generalized. The terms random-effect meta-regression and mixed-effect meta-regression are equivalent. Although calling one a random-effect model signals the absence
Meta-regression
Network of neurons with spiking signals
recurrent model, i.e. a neural network that is allowed to have complex feedback loops. A highly energy-efficient implementation of random neural networks
Random_neural_network
Protein folding hypothesis
1980s focused on models that could explain the shape of the energy landscape, a mathematical function that describes the free energy of a protein as a
Folding_funnel
Lowest possible energy of a quantum system or field
zero-point energy is also important for cosmology, and physics currently lacks a full theoretical model for understanding zero-point energy in this context;
Zero-point_energy
Mathematical model of the Big Bang
lambda (Λ), associated with dark energy, cold dark matter, denoted by CDM as well as ordinary matter. It is the simplest model that provides a reasonably good
Lambda-CDM_model
Type of large language model
dissemination. Training large-scale models also requires huge computational resources, contributing to increased energy consumption and environmental costs
Generative pre-trained transformer
Generative_pre-trained_transformer
Mathematical theory on behavior of connected clusters in a random graph
physicists since then. In a slightly different mathematical model for obtaining a random graph, a site is "occupied" with probability p or "empty" (in
Percolation_theory
Randall J. LeVeque Randall–Sundrum model Random close pack Random energy model Random laser Random matrix Random phase approximation Range (particle
Index_of_physics_articles_(R)
Concept in physics
the zero-energy universe model ("flat" or "Euclidean"), the total amount of energy in the universe is exactly zero: its amount of positive energy in the
Negative_energy
Model for generating observable data in probability and statistics
variable Y; A generative model can be used to "generate" random instances (outcomes) of an observation x. A discriminative model is a model of the conditional
Generative_model
does not look random, but it satisfies the definition of random variable. This is useful because it puts deterministic variables and random variables in
List of probability distributions
List_of_probability_distributions
Type of signal in signal processing
equal energy in each octave, is used for testing transducers such as loudspeakers and microphones. White noise is used as the basis of some random number
White_noise
Information theory quantity
often when developing mathematical models of wireless networks such as cellular networks. The complexity and randomness of certain types of wireless networks
Signal-to-interference-plus-noise ratio
Signal-to-interference-plus-noise_ratio
Model for the magnetization of single-domain ferromagnets
in 2009 for the magnetizations and the energy barriers for a given applied field. The Stoner–Wohlfarth model is a classic example of magnetic hysteresis
Stoner–Wohlfarth_model
British neuroscientist
statistical methods to model neuroimaging data and other random dynamical systems. Friston is a key architect of the free energy principle and active inference
Karl_J._Friston
Subset of artificial intelligence
decision tree is trained on random data from the training set. This random selection of RFR for training enables the model to reduce biased predictions
Machine_learning
Graphical representation of biomass or biomass productivity
An ecological pyramid (also trophic pyramid, Eltonian pyramid, energy pyramid, or sometimes food pyramid) is a graphical representation designed to show
Ecological_pyramid
Statistical Markov model
described discriminative model is the linear-chain conditional random field. This uses an undirected graphical model (aka Markov random field) rather than the
Hidden_Markov_model
Mathematical concept
appropriate energy function. This is the Hammersley–Clifford theorem. What follows is a formal definition for the special case of a random field on a lattice
Gibbs_measure
physics and probability, the filters, random fields, and maximum entropy (FRAME) model is a Markov random field model (or a Gibbs distribution) of stationary
Filters, random fields, and maximum entropy model
Filters,_random_fields,_and_maximum_entropy_model
Model in network science
The Bianconi–Barabási model is a model in network science that explains the growth of complex evolving networks. This model can explain that nodes with
Bianconi–Barabási_model
Network whose degree distribution follows a power law
strongly scale-free. Random graph – Graph generated by a random process Erdős–Rényi model – Two closely related models for generating random graphs Non-linear
Scale-free_network
Quantitative methods used to simulate climate
transfer model treats the Earth as a single point and averages outgoing energy. This can be expanded vertically (radiative-convective models) and horizontally
Climate_model
Idealization in polymer thermodynamics
the random walk model, where each step taken in a random direction is independent of the directions taken in the previous steps, forming a random coil
Kuhn_length
Machine learning technique
gradient-boosted trees; it usually outperforms random forest. As with other boosting methods, a gradient-boosted trees model is built in stages, but it generalizes
Gradient_boosting
Paradigm in machine learning that uses no classification labels
moments, the unknown parameters (of interest) in the model are related to the moments of one or more random variables, and thus, these unknown parameters can
Unsupervised_learning
index Random assignment Random compact set Random data – see randomness Random effects estimation – see Random effects model Random effects model Random element
List_of_statistics_articles
Austrian mathematician and theoretical physicist (1844–1906)
one can say that the random motion (the agitation) of the dice, like the chaotic collisions of molecules because of thermal energy, causes the less probable
Ludwig_Boltzmann
Graphical models have become powerful frameworks for protein structure prediction, protein–protein interaction, and free energy calculations for protein
Graphical models for protein structure
Graphical_models_for_protein_structure
Form of artificial neural network
memory. The Sherrington–Kirkpatrick model of spin glass, published in 1975, is the Hopfield network with random initialization. Sherrington and Kirkpatrick
Hopfield_network
Ensemble of states at a constant temperature
connection's mechanical influence on the system is modeled within the system. When the total energy is fixed but the internal state of the system is otherwise
Canonical_ensemble
AI that generates content
models, regulating for transparency of these models, regulating their energy and water usage, encouraging researchers to publish data on their models'
Generative_AI
American anthropologist
metabolism known as the "constrained daily energy expenditure model". According to this theory, total daily energy expenditure is not simply the sum of separate
Herman_Pontzer
Statistical model for a binary dependent variable
In statistics, a logistic model (or logit model) is a statistical model that models the log-odds of an event as a linear combination of one or more independent
Logistic_regression
Theorem in classical statistical mechanics
a system to its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition
Equipartition_theorem
This model is known as the ice model (as opposed to an ice-type model). Slater argued that KDP could be represented by an ice-type model with energies ϵ
Ice-type_model
Arrangement of points on a sphere
millennium has been on local optimization methods applied to the energy function, although random walks have made their appearance: constrained global optimization
Thomson_problem
Personality model consisting of five broad dimensions
personality trait model or five-factor model (FFM), sometimes called by the mnemonic acronym OCEAN or CANOE, is a scientific model for measuring and describing
Big_Five_personality_traits
Model used in risk analysis
The Swiss cheese model of accident causation is a model used in risk analysis and risk management. It likens human systems to multiple slices of Swiss
Swiss_cheese_model
Polymer with rubber-like elastic properties
interatomic bond distances (energy elasticity), elastomer elasticity is entropy-driven. In an unstressed state, polymer chains assume random coiled configurations
Elastomer
Acceleration phenomenon of oft-reflected charged particles
particles gain non-thermal energies in astrophysical shock waves. It plays a very important role in many astrophysical models, mainly of shocks including
Fermi_acceleration
Random energy exchange from thermal masses
fluctuation noise, arises from the random exchange of energy between a thermal mass and its surrounding environment. This energy is quantized in the form of
Phonon_noise
Statistical distribution for dependence between random variables
interval [0, 1]. Copulas are used to describe / model the dependence (inter-correlation) between random variables. Their name, introduced by applied mathematician
Copula_(statistics)
Natural interconnection of food chains
Some of the organic matter eaten by heterotrophs, such as sugars, provides energy. Autotrophs and heterotrophs come in all sizes, from microscopic to many
Food_web
Solvable physics model
physics and black hole physics, the Sachdev–Ye–Kitaev (SYK) model is an exactly solvable model initially proposed by Subir Sachdev and Jinwu Ye, and later
Sachdev–Ye–Kitaev_model
Flow of energy through food chains in ecological energetics
Energy flow is the flow of energy through living things within an ecosystem. All living organisms can be organized into producers and consumers, and those
Energy_flow_(ecology)
Discrete probability distribution
accidentally killed by horse kicks could be well modeled by a Poisson distribution.. A discrete random variable X is said to have a Poisson distribution
Poisson_distribution
2025 multimodal model by OpenAI
multimodal large language model developed by OpenAI and the fifth in its series of generative pre-trained transformer (GPT) foundation models. Preceded in the
GPT-5
Symmetry in statistical physics
It relates the free energy of a two-dimensional square-lattice Ising model at a low temperature to that of another Ising model at a high temperature
Kramers–Wannier_duality
Random walk with heavy-tailed step lengths
biological flight can also apparently be mimicked by other models such as composite correlated random walks, which grow across scales to converge on optimal
Lévy_flight
Elementary particle or quantum of light
electron–positron annihilation). In a quantum mechanical model, electromagnetic waves transfer energy in photons with energy proportional to frequency ( ν {\displaystyle
Photon
Stochastic process modeling random walk with friction
This model has been used to characterize the motion of a Brownian particle in an optical trap. At equilibrium, the spring stores an average energy ⟨ E
Ornstein–Uhlenbeck_process
Excess energy at the surface of a material relative to its interior
In surface science, surface energy (also interfacial free energy or surface free energy) quantifies the disruption of intermolecular bonds that occurs
Surface_energy
Organisms that obtain energy by the oxidation of electron donors in their environments
A chemotroph is an organism that obtains energy by the oxidation of electron donors in their environments. These molecules can be organic (chemoorganotrophs)
Chemotroph
Stochastic volatility model used in derivatives markets
In mathematical finance, the SABR model is a stochastic volatility model, which attempts to capture the volatility smile in derivatives markets. The name
SABR_volatility_model
Continuous probability distribution
distribution /ˈwaɪbʊl/ is a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time
Weibull_distribution
Image segmentation algorithm
assigned to the label for which it is most likely to send a random walker. The image is modeled as a graph, in which each pixel corresponds to a node which
Random_walker_algorithm
Description of physical properties at the atomic and subatomic scale
quantum mechanical model to create a result for a related but more complicated model by (for example) the addition of a weak potential energy. Another approximation
Quantum_mechanics
Type of computer memory
Static random-access memory (static RAM or SRAM) is a type of random-access memory (RAM) that uses latching circuitry (flip-flop) to store each bit. SRAM
Static_random-access_memory
Measure of covariance of components of a random vector
square matrix giving the covariance between each pair of elements of a given random vector. Intuitively, the covariance matrix generalizes the notion of variance
Covariance_matrix
Elementary particle involved with rest mass
chance that the observed decay signatures are due to just background random Standard Model events – i.e., that the observed number of events is more than five
Higgs_boson
Choice between two or more discrete alternatives
Logit Model - Suitable for route choice problems. Generalized Extreme Value Model - General class of model, derived from the random utility model to which
Discrete_choice
Probability distribution of energy states of a system
multinomial logit model. As a discrete choice model, this is very well known in economics since Daniel McFadden made the connection to random utility maximization
Boltzmann_distribution
Probabilistic optimization technique and metaheuristic
much lower energy than a random state. Therefore, as a general rule, one should skew the generator towards candidate moves where the energy of the destination
Simulated_annealing
Subset of variables that contains all the useful information
probabilistic graphical model such as a Bayesian network or Markov random field. A Markov blanket of a random variable Y {\displaystyle Y} in a random variable set
Markov_blanket
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RANDOM ENERGY-MODEL
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