We extend the Carne–Varopoulos upper bound on the probability transitions of a Markov chain to a certain class of nonreversible processes by introducing the definition of a “centering measure.” In the case of random walks on a group, we study the connections between different notions of centering.
Pierre Mathieu. "Carne–Varopoulos bounds for centered random walks." Ann. Probab. 34 (3) 987 - 1011, May 2006. https://doi.org/10.1214/009117906000000052