A survey of random processes with reinforcement

By Robin Pemantle. 2006

559 citations recorded by the source corpus.

The models surveyed include generalized Polya 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.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/567342adbe715d30a5ec83a6e51c14078e2917a5

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Citations in the corpus

RECURRENCE OF EDGE-REINFORCED RANDOM WALK ON A TWO-DIMENSIONAL GRAPH (2007, background): “For a recent overview of general processes with reinforcement, we refer the reader to [11].”
Runaway Feedback Loops in Predictive Policing (2017, methodology): “Urn models (especially the Pólya-Eggenberger urns) have a long history in machine learning, but notably also in reinforcement learning [11], where they have been used, starting with the work of Erev and Roth [1], as a way to model how bounded-rationality players in a game might interact with each ot”
On a preferential attachment and generalized Pólya’s urn model (2012, background): “(A detailed review of a number of other interesting results on Pólya’s urn processes and on reinforcement processes in general is provided in the survey [22].”
Random Graphs and Complex Networks (2016, background): “More recent discussions on exchangeable random variables and their properties can be found in [8] and [188], the latter focussing on random walks with self-interaction, where exchangeability is a crucial tool.”
Random walks and diffusion on networks (2016, background): “RWs [4, 70, 71], zero-range processes [72], multiplicative random processes [73, 105 74], adaptive RWs (including reinforced RWs [75]), branching RWs [76], Lévy 106 flights [34, 35], elephant RWs [77], quantum walks [78, 79], intermittent RWs 107 [80], persistent RWs [81], starving RWs [82–84], mort”
Growth of preferential attachment random graphs via continuous-time branching processes (2007, unknown): “[17]).”
A martingale approach for the elephant random walk (2017, methodology): “Baur and Bertoin [1] extensively used the connection to Pólya-type urns [17] as well as two functional limit theorems for multitype branching processes due to Janson [10], see also [4].”