A survey of random processes with reinforcement

Abstract

The models surveyed include generalized Pólya urns, reinforced random walks, interacting urn models, and continuous reinforced processes. Emphasis is on methods and results, with sketches provided of some proofs. Applications are discussed in statistics, biology, economics and a number of other areas.

Published at http://dx.doi.org/10.1214/07-PS094 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (7)

• Emergence of scaling in random networks
• Analytic urns
• Bayesian analysis for reversible Markov chains
• On the transience of processes defined on Galton--Watson trees
• Linearly edge-reinforced random walks
• Edge-reinforced random walk on a ladder
• Avoiding defeat in a balls-in-bins process with feedback

Cited by in corpus (175)

• Random walks and diffusion on networks
• Network dynamics of innovation processes
• Modeling and Predicting Popularity Dynamics via Reinforced Poisson Processes
• Elephant Random Walks and their connection to Pólya-type urns
• A martingale approach for the elephant random walk
• Localization transition induced by learning in random searches
• On Gradient-Based Learning in Continuous Games
• A dynamic model of time-dependent complex networks
• The Spacey Random Walk: a Stochastic Process for Higher-order Data
• Vertex-reinforced random walk on Z eventually gets stuck on five points
• Interacting discovery processes on complex networks
• Solvable random walk model with memory and its relations with Markovian models of anomalous diffusion
• Recurrence of edge-reinforced random walk on a two-dimensional graph
• Localization for Linearly Edge Reinforced Random Walks
• A generalized Polya's urn with graph based interactions
• Recurrence and transience for the frog model on trees
• An asymptotic result for Brownian polymers
• On a preferential attachment and generalized Pólya's urn model
• Random walks in random Dirichlet environment are transient in dimension $d\ge 3$
• On the stability of two-chunk file-sharing systems
• Random Dirichlet environment viewed from the particle in dimension $d\ge 3$
• Role of Depletion on the Dynamics of a Diffusing Forager
• A stochastic approximation approach to quasi-stationary distributions on finite spaces
• Joint Modeling of Event Sequence and Time Series with Attentional Twin Recurrent Neural Networks
• Generalized gamma approximation with rates for urns, walks and trees
• Reinforced walks in two and three dimensions
• Robust analysis of preferential attachment models with fitness
• Random walks with preferential relocations and fading memory: a study through random recursive trees
• Random walkers with extreme value memory: modelling the peak-end rule
• A Polya Contagion Model for Networks
• By Force of Habit: Self-Trapping in a Dynamical Utility Landscape
• A theoretical model for the associative nature of conference participation
• Synchronization via interacting reinforcement
• On a class of random walks with reinforced memory
• Interacting generalized Friedman's urn systems
• Dynamics of vertex-reinforced random walks
• Synchronization of Reinforced Stochastic Processes with a Network-based Interaction
• Coexistence in preferential attachment networks
• Large deviations for Generalized Polya Urns with arbitrary urn function
• Correlation function for generalized Pólya urns: Finite-size scaling analysis
• Generalized Polya urns via stochastic approximation
• Fluctuations in interacting particle systems with memory
• Non-selective evolution of growing populations
• Excited random walks: results, methods, open problems
• Large deviations in models of growing clusters with symmetry-breaking transitions
• Pólya Urn Schemes with Infinitely Many Colors
• General Tensor Spectral Co-clustering for Higher-Order Data
• The true reinforced random walk with bias
• The Dynamics of Knowledge Acquisition via Self-Learning in Complex Networks
• Generalized Interacting Urn Models
• Inference for graphs and networks: Extending classical tools to modern data
• Joint statistics of space and time exploration of $1d$ random walks
• Growth-induced breaking and unbreaking of ergodicity in fully-connected spin systems
• Emergence of linguistic conventions in multi-agent reinforcement learning
• Greedy walk on the real line
• Graph-based Polya's urn: completion of the linear case
• Central limit theorems for an Indian buffet model with random weights
• Some particular self-interacting diffusions: Ergodic behaviour and almost sure convergence
• Interacting reinforced stochastic processes: statistical inference based on the weighted empirical means
• Phase transitions for random geometric preferential attachment graphs
• Attraction time for strongly reinforced walks
• A model for the Twitter sentiment curve
• Rank-driven Markov processes
• Detection of phase transition in generalized Pólya urn in information cascade experiment
• Large Deviations Theory of Increasing Returns
• Ergodic Properties of weak Asymptotic Pseudotrajectories for Set-valued Dynamical Systems
• Unlearnable Games and "Satisficing'' Decisions: A Simple Model for a Complex World
• Dynamic Hawkes Processes for Discovering Time-evolving Communities' States behind Diffusion Processes
• The simple harmonic urn
• Emergence of Social Structures via Preferential Selection
• Greedy Random Walk
• Infinite-color randomly reinforced urns with dominant colors
• Interacting Urn Models
• Self-repelling random walk with directed edges on Z
• Random Polymers and Generalized Urn Processes
• Preferential attachment with location-based choice: Degree distribution in the noncondensation phase
• Networks of reinforced stochastic processes: asymptotics for the empirical means
• Convergence in a multidimensional randomized Keynesian beauty contest
• The Rescaled Polya Urn: local reinforcement and chi-squared goodness of fit test
• Modeling Event Propagation via Graph Biased Temporal Point Process
• Localisation in a growth model with interaction
• Condensation in preferential attachment models with location-based choice
• Self-repelling diffusions on a Riemannian manifold
• Random walk with barycentric self-interaction
• Edge-reinforced random walk, Vertex-Reinforced Jump Process and the supersymmetric hyperbolic sigma model
• Phase transition of social learning collectives and "Echo chamber"
• A simple rank-based Markov chain with self-organized criticality
• Extensive Condensation in a model of Preferential Attachment with Fitnesses
• On the duration and intensity of cumulative advantage competitions
• Fluctuations of the local times of the self-repelling random walk with directed edges
• Characterization of exchangeable measure-valued Pólya urn sequences
• Generalized Rescaled Polya urn and its statistical applications
• Inverting the Ray-Knight identity on the line
• Urns with simultaneous drawing
• Ant foraging and minimal paths in simple graphs
• A theory of maximum likelihood for weighted infection graphs
• Non-convergence of proportions of types in a preferential attachment graph with three co-existing types
• Decision-making with distorted memory: Escaping the trap of past experience
• Urn models with two types of strategies
• Cooperation in Microbial Populations: Theory and Experimental Model Systems
• Current fluctuations of a self-interacting diffusion on a ring
• Vertex reinforced random walks with exponential interaction on complete graphs
• Periodic Pólya urns and an application to Young tableaux
• Recurrence for vertex-reinforced random walks on Z with weak reinforcements
• Stability and evolution of synonyms and homonyms in signaling game
• The Evolution of Complex Networks: A New Framework
• On the dual nature of adoption processes in complex networks
• VRRW on complete-like graphs: Almost sure behavior
• Boundary effect in competition processes
• Reinforcement learning from comparisons: Three alternatives is enough, two is not
• Dynamic Models of Reputation and Competition in Job-Market Matching
• Reinforcement Learning with Policy Mixture Model for Temporal Point Processes Clustering
• Bayesian Allocation Model: Inference by Sequential Monte Carlo for Nonnegative Tensor Factorizations and Topic Models using Polya Urns
• Wages and Capital returns in a generalized Pólya urn
• Time-Dependent Urn Models reproduce the full spectrum of novelties discovery
• Asymptotics of generalized Pólya urns with non-linear feedback
• Networks of reinforced stochastic processes: a complete description of the first-order asymptotics
• Random walks avoiding their convex hull with a finite memory
• Time-dependent Pólya urn
• Stability of a growth process generated by monomer filling with nearest-neighbour cooperative effects
• Geometric preferential attachment in non-uniform metric spaces
• Recurrence of horizontal-vertical walks
• DAG-type Distributed Ledgers via Young-age Preferential Attachment
• Feedback Effects in Repeat-Use Criminal Risk Assessments
• Generating Preferential Attachment Graphs via a Pólya Urn with Expanding Colors
• A balanced excited random walk
• A note on multi-type cookie random walk on integers
• Persistence exponents of self-interacting random walks
• Spin systems with hyperbolic symmetry: a survey
• Compounding Injustice: History and Prediction in Carceral Decision-Making
• Power law Polya's urn and fractional Brownian motion
• Interacting non-linear reinforced stochastic processes: synchronization and no-synchronization
• Strong Convergence of Infinite Color Balanced Urns Under Uniform Ergodicity
• General random walk in a random environment defined on Galton-Watson trees
• Stuck walks: A conjecture of Erschler, Tóth and Werner
• Information cascade on networks and phase transitions
• Weakly self-interacting velocity jump processes for bacterial chemotaxis and adaptive algorithms
• A random recursive tree model with doubling events
• Self-interacting processes via Doob conditioning
• Random walk attachment graphs
• Preferential attachment with fitness dependent choice
• Survey on Modeling Intensity Function of Hawkes Process Using Neural Models
• Curiosities regarding waiting times in Pólya's urn model
• Percolation Threshold Results on \Erdos-\Renyi Graphs: an Empirical Process Approach
• Exploring the Ant Mill: Numerical and Analytical Investigations of Mixed Memory-Reinforcement Systems
• A Polya Urn Document Language Model for Improved Information Retrieval
• A Class of Multi-particle Reinforced Interacting Random Walks
• Stochastic Approximation, Cooperative Dynamics and Supermodular Games
• Ergodicity of self-attracting motion
• Modelling savings behavior of agents in the kinetic exchange models of market
• A class of non homogeneous self interacting random processes with applications to learning in games and vertex-reinforced random walks
• Stationary distributions for diffusions with inert drift
• Queue-length Variations In A Two-Restaurant Problem
• On some generalized reinforced random walks on integers
• Limit theorems for vertex-reinforced jump processes on regular trees
• Self-interacting diffusions IV: Rate of convergence
• Diffusion constants and martingales for senile random walks
• The ODE method for some self-interacting diffusions on non-compact spaces
• Pólya urns with immigration at random times
• One-dimensional System Arising in Stochastic Gradient Descent
• Time-dependent balls and bins model with positive feedback
• Modeling trend progression through an extension of the Polya Urn Process
• Random Additions in Urns of Integers
• Ulam's History-dependent Random Adding Process
• Random walkers on a deformable medium
• Vertex-reinforced jump process on the integers with nonlinear reinforcement
• Two repelling random walks on $\mathbb{Z}$
• Rate of Convergence and Large Deviation for the Infinite Color Pólya Urn Schemes
• Urn models with random multiple drawing and random addition
• Fragility of non-convergence in preferential attachment graphs with three types
• A scaling limit for the degree distribution in sublinear preferential attachment schemes
• Weighing the "Heaviest" Polya Urn
• Anomalous Diffusion and Emergent Universality in Coupled Memory-Driven Systems
• How Vertex reinforced jump process arises naturally
• Reinforced Brownian Motion on the Half-Line