# Reinforced random walks

Vertex-reinforced random walk robin pemantle 1 dept of statistics uc berkeley 2 abstract: this paper considers a class of non-markovian discrete-time random. Recent developments in random walks: reinforced random walk on two-dimensional graphs : p moerters: intersections of random walks in supercritical dimensions. Topics in self-interacting random walks reza rastegar iowa state university chapter 3 limit laws for a directionally reinforced random walk 24. Edge-reinforced random walk on a ladder merkl, f rolles, sww published in: the annals of probability doi: 101214/009117905000000396 published: 01/01/2005. Rsifroyalsocietypublishingorg research cite this article: ma q, johansson a, tero a, nakagaki t, sumpter djt 2013 current-reinforced random walks for constructing.

Random walks under slowly varying moment conditions on groups of polynomial volume growth, with laurent saloff-coste proceedings of the conference . We define a reinforced urn process (rup) to be a reinforced random walk on a state space of urns and we show its partial exchangeability when it is recurrent, a rup. A random walk is a mathematical object, in brain research, random walks and reinforced random walks are used to model cascades of neuron firing in the brain. 1 introduction reinforced random walks have been studied extensively since the introduction of the (linearly)-reinforced random walk of coppersmith and diaconis [6.

Vrrw on complete-like graphs: almost sure behavior limic, vlada and volkov, stanislav, the annals of applied probability, 2010 vertex-reinforced random walk on ℤ. 1 introduction and summary coppersmith and diaconis (1987) have initiated the study of a class of processes called reinforced random walks see also diaconis (1988. Pdf | we describe and analyze how reinforced random walks can eventually localize, ie only visit finitely many sites after introducing vertex and edge self. Shortest paths through a reinforced random walk 2 a path increases with the number of ants that chose the same path. Strongly reinforced vertex-reinforced-random-walk on the complete graph michel benaim, olivier raimond, bruno schapira 1 introduction this paper considers a ertex.

The process itself is a vertex-reinforced random walk, and its discrete dynamics are related to a continuous dynamical system we analyze the. Non-classical random walks outline 1 classical random walks 2 random walks in random environments 3 reinforced random walks 4 excited random walks jonathon peterson 4. Edge-reinforced random walks produce a co-evolution of the network with the dynamics of the walkers at time t the walker is on the red node and has already visited.

## Reinforced random walks

We discuss and disprove a conjecture of pemantle concerning vertex-reinforced random walks the setting is a general theory of non-markovian discrete-time random 4. Investigating mixed memory-reinforcement models for random walks ria das, reinforced random walks mean ow rate (i ij) equation based on edge weights (ma q. The branching-ruin number and the critical parameter of once-reinforced random walk on trees, with a collevecchio and v sidoravicius, 2017, preprint. A discrete random walk that avoids previously visited vertices for an exponentially distributed time interval to the theory of reinforced random walks.

- We study vertex-reinforced-random-walk on the complete graph with weights of the form $w(n)=n^\alpha$, with $\alpha1$ unlike for the edge-reinforced-random-walk.
- The weakly reinforced random walk (wrrw) on the one-dimensionalinteger lattice zstarts from the origin of the lattice and at each step it jumps to aneighbouring site.

This simulation is made using a a new parallel version of the current reinforced-random walk model implemented in c by kristoffer jonsson and david jäderberg. 568 r durrett et al the question is whether {xn} (which by itself is non-markovian) is recurrent or transient we only consider the case when g is a regular b-ary tree. Request pdf on researchgate | urn schemes and reinforced random walks | we define a reinforced um process (rup) to be a reinforced random walk on a state space of. A once edge-reinforced random walk on a galton–watson tree is transient almost surely this extends a result of durrett, kesten and limic (2002, probab.