Cutoff of the simple exclusion process with inhomogeneous conductances

2024/09/24 by Shangjie Yang, Yang, Shangjie · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum Mechanics and Applications #Cold Atom Physics and Bose-Einstein Condensates

paper · pdf · doi:10.48550/arxiv.2409.16337

Abstract

In this paper, we study the mixing time of the simple exclusion process with k particles in the line segment [1, N] with conductances c^(N)(x, x+1)_1≤ x0 is the rate of swapping the contents of the two sites x and x+1. Writing r^(N)(x, x+1) := 1/c^(N)(x, x+1), under the assumption \limsup_{N→ ∞} (1)/(N)sup_{1lt; m ≤ N} | ∑_x=2^m r^(N)(x-1, x)- (m-1) | = 0 , and some further assumptions on r^(N)(x, x+1)_{x ∈ ℕ} and k, we prove that around time (1+o(1)) (2 π²)^-1 N² log k, the total variation distance to equilibrium of the simple exclusion process drops abruptly from 1 to 0.

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• Product-Form Distribution and Reversibility of Inhomogeneous Symmetric Simple Exclusion Process with Open Boundaries

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