6 papers
Mixing times of step-reinforced random walks
Yuval Peres, Shuo Qin
We study the mixing time of a non-Markovian process, the step-reinforced random walk (SRRW) on a finite group. This process differs from a classical random walk in that at each int…
Transition probabilities of step-reinforced random walks
Yuval Peres, Shuo Qin
The step-reinforced random walk (SRRW), where each step may replicate a randomly chosen past step, exhibits complex dependencies on the history. This paper introduces a generalized…
How reactive gambling can backfire: ruin probability is increasing in , Hölder continuous in initial fortune
Aditya Guha Roy, Yuval Peres, Shuo Qin +1
A gambler with an initial fortune starts by betting a dollar, then doubles the bet after every win and halves the bet after every loss. Let be the probability of w…
How two elephants can learn from each other
Rafik Aguech, Shuo Qin
We consider a two-elephant walking model in which the elephants interact dynamically. At each time step, each elephant determines its next move randomly based on its partner's past…
Step-reinforced random walks and one-half
Shuo Qin
Under suitable moment assumptions, we show that a genuinely d-dimensional step-reinforced random walk undergoes a phase transition between recurrence and transience in dimensions $…
Interacting urn models with strong reinforcement
Shuo Qin
For the interacting urn model with polynomial reinforcement, it has been conjectured that almost surely one color monopolizes all the urns if the interaction parameter . We di…