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Estimating Expected Convergence Time for Random Walk in Combined Expander Graphs

score 90 · Answer 1 · 2026-03-29 04:33:53

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Estimating Expected Convergence Time for Random Walk in Combined Expander Graphs

Published on 29 Mar 2026 - 4:33

score 47 · Answer 2 · 2026-03-29 08:15:56

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$(X_{k})_{k }$ are IID, $P[X_{k}=1]=P[X_{k}=-1]=\frac{1}{2}$; $S_{n}=\sum_{k\leq n}X_{k}$ , $\tau=\inf\{n:S_{n}\in\{-a,b\}\}$. $E[\tau^{2}]=$?

Published on 29 Mar 2026 - 8:15

score 80 · Answer 3 · 2023-12-15 05:31:33

80

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63

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List Question

Estimating Expected Convergence Time for Random Walk in Combined Expander Graphs

$(X_{k})_{k }$ are IID, $P[X_{k}=1]=P[X_{k}=-1]=\frac{1}{2}$; $S_{n}=\sum_{k\leq n}X_{k}$ , $\tau=\inf\{n:S_{n}\in\{-a,b\}\}$. $E[\tau^{2}]=$?

2 person Symmetric Random Walk on a line separated by some distance.

Random Walks and Optimal Return Paths in a Collatz-Inspired Tree of Odd Integers

Random walks and Markov chains

Probability for collisions in a 2D random walk scenario

Probability of random walk reaching one threshold before another using recurrence relation

Take a random walk on a Christmas tree, starting at the top. What is the probability of returning to the top?

Expectation of hitting time for the asymmetric random walk via Martingale

How often do we expect a random walk with decreasing step size to cross $0$?

A question related to Lovasz Simonovits curve

Left tail bound for stopping time of a gaussian random walk

Projected random walk on sphere converges to Brownian motion?

How is Chaos defined in Math?

Generate random numbers using SDE of the Legendre process

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