37 citations · 126 across the 31 of their papers we have counts for
27 papers · 1 filter
Once-Reinforced and Self-Interacting Random Walks beyond exchangeability
Andrea Collevecchio, Pierre Tarrès
We present the first rigorous quantitative analysis of once-reinforced random walks (ORRW) on general graphs, based on a novel change of measure formula.~This enables us to prove l…
Finding pure Nash equilibria in large random games
Andrea Collevecchio, Tuan-Minh Nguyen, Ziwen Zhong
Best Response Dynamics (BRD) is a class of strategy updating rules to find Pure Nash Equilibria (PNE) in a game. At each step, a player is randomly picked, and the player switches…
Strongly vertex-reinforced jump process on graphs with bounded degree
Andrea Collevecchio, Tuan-Minh Nguyen
We study asymptotic behaviours of a non-linear vertex-reinforced jump process defined on an arbitrary infinite graph with bounded degree. We prove that if the reinforcement functio…
A class of non-reversible hypercube long-range random walks and Bernoulli autoregression
Andrea Collevecchio, Robert C. Griffiths
We study a large class of long-range random walks which take values on the vertices of an N dimensional hypercube. These processes are connected with multivariate Bernoulli autoreg…
Long range one-cookie random walk with positive speed
Andrea Collevecchio, Kais Hamza, Tuan-Minh Nguyen
We study one-dimensional excited random walks with non-nearest neighbor jumps. When the process is at a vertex that has not been visited before, its next transition has a positive…
Limit theorems and ergodicity for general bootstrap random walks
A. Collevecchio, K. Hamza, M. Shi +1
Given the increments of a simple symmetric random walk , we characterize all possible ways of recycling these increments into a simple symmetric random walk $(Y_n)_{…