Cutoffs for exclusion and interchange processes
on finite graphs Coauthor: Joe P. Chen We prove a general theorem on cutoff for the exclusion and the interchange processes on finite graphs G_N, most under the natural assumption that the graphs converge geometrically and spectrally to a compact metric measure space. We show that both processes, under the aforementioned assumption, present cutoffs at times t_N= (2 \gamma_1^N)^{-1} \log |V_N|, where \gamma_1^N is the spectral gap of the simple random walk on G_N. We exemplify with the particular cases of these processes on discrete grids and tori, fractal approximations, hypercubes, and powers of cycles (L-adjacent transposition shuffle). |
See also the work where we prove cutoffs for exclusion processes with Glauber dynamics happening at the boundary vertices of the graphs:
Cutoffs for exclusion processes on graphs with open boundaries
Coauthor: Joe P. Chen and Milton Jara.
Coauthor: Joe P. Chen and Milton Jara.