In this talk I will show how one can use stochastic duality to close evolution equations for time-dependent correlation functions and how to use these equations to obtain $L^∞$ bounds for these functions through a random walk approach.

I will give some examples of microscopic models for which this technique can be applied and obtain for those the decay of 2-point correlation functions. If time allows, I will explain the main difficulties for the case of $k$-point correlation functions for $k > 2$.

Based on joint works with Chiara Franceschini, Patrícia Gonçalves and Milton Jara.