… so t_x(e) = 2 ln e^-1 /F². If the Markov chain has symmetric transitions with constant probability (P (x, y) = P (y, x) = 0 or p, if x ¹ y ) then p_x = 1/d and with d (S) the number of transitions out of S (the cutset of S).
To compute bound in general the mixing time define for each ordered pair (x, y) of states a canonical path g_xy made up of legal transitions. Let G := {g_xy : x, y Î U}.Writing e = (x, y) for the transition x ® y, let the following. Then a theorem states.