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math.PR2025
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…
math.PR2024
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…
math.PR2024
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…