Compute a histogram of the time for a random walk, with the walker taking steps of ±1 to return to his/her starting position

Statistics Nov 18, 2020

Compute a histogram of the time for a random walk, with the walker taking steps of ±1 to return to his/her starting position. If T is the return time show that P ( T = t/2) ≈ /ζ(3/2), where the normalisation constant ζ(3/2) ≈ 2.61 is the Riemann zeta function. Use this fact to show that a random walker will return to his/her starting position with probability arbitrarily close to 1, but the expected return time is infinite.