arXiv subjects

Linzhi Yang

Publications and source records attributed to Linzhi Yang.

2 recordsLinked to original sources

arXiv2026

Scaling limit of additive functionals for reversible non-gradient exclusion process: critical cases

For the reversible speed-change exclusion process $(\eta_t)_{t \geq 0}$ in $\mathbb{Z}^d$, we study the scaling limit of additive functionals ${\Gamma_t(f) = \int_0^t f(\eta_s)\, \mathrm{d} s}$. Concerning the local centered function $f$, the previous work [Commun. Math. Phys. 104, 1-19, 1986] by Kipnis and Varadhan and [Comm. Pure Appl. Math., 66: 649-677, 2013] by Gon{\c{c}}alves and Jara respectively covered the cases $d \geq 3$ and $d=1$. The present paper completes the missing part $d=2$, and also develops the theory for functions with higher degree. The novelty is a quantitative homogenization of the resolvent, which allows to overcome the obstacle of correlation function in non-gradient models.

math.PR↗

arXiv2025

Relaxation to equilibrium of conservative dynamics II: non-gradient exclusion processes

For the speed-change exclusion process on $\mathbb{Z}^d$ reversible with respect to the product Bernoulli measure, we prove that its semigroup $P_t$ satisfies a variance decay $\operatorname{Var}[P_t u] = C_u t^{-\frac{d}{2}} + o(t^{-\frac{d+\delta}{2}})$ for every local function $u$, with the constant $C_u$ explicitly characterized. This extends the result of Janvresse, Landim, Quastel and Yau in [Ann. Probab. 27(1) 325--360, 1999] to a non-gradient model. The proof combines the regularization argument in the previous work, and the chaos expansion in [Markov Process. Related Fields, 5(2) 125--162, 1999] by Bertini and Zegarlinski, via a new input from the homogenization theory.

math.PR↗