Step-reinforced random walks on finite groups converge exponentially to uniform; on cycles mixing time jumps from logarithmic to polynomial at alpha=1/2, while on hypercubes reinforcement slows mixing with cutoff at d log d over F(alpha)(1-alpha).
Asymptotic normality of superdiffusive step-reinforced random walks
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Elephant random walks on d-regular infinite trees have asymptotic speed (d-2)/d independent of memory parameter p, with p-dependent upper bounds on convergence rate that exhibit a phase transition at p_d = (d+1)/(2d).
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Mixing times of step-reinforced random walks
Step-reinforced random walks on finite groups converge exponentially to uniform; on cycles mixing time jumps from logarithmic to polynomial at alpha=1/2, while on hypercubes reinforcement slows mixing with cutoff at d log d over F(alpha)(1-alpha).
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Elephant random walks on infinite Cayley trees
Elephant random walks on d-regular infinite trees have asymptotic speed (d-2)/d independent of memory parameter p, with p-dependent upper bounds on convergence rate that exhibit a phase transition at p_d = (d+1)/(2d).
- A Poincar\'e Inequality and Exponential Decay for the Elephant Random Walk