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math.PR2025
Survival probability in reactive gambling: monotonicity, singularity, and Hölder continuity
Aditya Guha Roy, Yuval Peres, Shuo Qin +1
A gambler starts with fortune and unit bet, then aims to double the bet after every win and halve it after every loss, while the actual bet is capped by the current fortune. Ea…
math.PR2025
Convergence rate of -relaxation on a graph to a -harmonic function with given boundary values
Chenyu Gan, Yuval Peres, Junchi Zuo
We analyze the following dynamics on a connected graph with vertices. Let , where the set of interior vertices is disjoint from the s…
math.PR2025
Convergence rate of -energy minimization on graphs: sharp polynomial bounds and a phase transition at
Gideon Amir, Fedor Nazarov, Yuval Peres
We consider the following dynamics on a connected graph with vertices. Given and an initial opinion profile , at each integer step a un…