Fast sampling via spectral independence beyond bounded-degree graphs
In this talk, we will discuss how to relax the bounded-degree assumption that has so far been important in establishing and applying spectral independence. Previous methods for avoiding degree bounds rely on using L^p-norms to analyse correlation decay on graphs with bounded connective constant (Sinclair et al., FOCS’13). The non-linearity of L^p-norms is one of the key obstacles to apply these results and bound spectral independence. We instead capture the L^p-analysis recursively by amortisation, using appropriate combinatorial information of the correlation-decay recurrence; our method generalises previous analyses that applied only to bounded-degree graphs.