Edward Crane

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math.PR2025

Recurrence, transience and anti-concentration of Rademacher random walks

Satyaki Bhattacharya, Edward Crane, Tom Johnston

The Rademacher random walk associated with a deterministic sequence $(a_{n})_{n \geq 1}$ is the walk which starts at zero and, at step $i$ , independently steps either up or down by $…

math.PR2024

Weak lumping of left-invariant random walks on left cosets of finite groups

Edward Crane, Álvaro Gutiérrez, Erin Russell +1

Let $G$ be a finite group and let $H$ be a subgroup of $G$ . The left-invariant random walk driven by a probability measure $w$ on $G$ is the Markov chain in which from any state $x…