证明了N. 1D接触过程的Konno

快速搅拌下接触过程临界值的渐近性态

Asymptotic behaviour of the critical value for the contact process with rapid stirring

我们研究了在$d\geq 3$维度上的晶格$\Z^d$上快速搅拌的接触过程的行为。Konno和Katori早先研究了这个过程，他们证明了当搅拌速率接近无穷大时临界值的收敛速度的结果。%Katori改进了$d\geq 3$中Katori的结果，并产生了临界值必须位于的区间。本文改进了Konno和Kattori的结果，建立了维数为$d\geq 3$的临界值的尖锐渐近性.

Improved asymptotic estimates for the contact process with stirring

We study the contact process with stirring on $\mathbb{Z}^d$. In this process, particles occupy vertices of $\mathbb{Z}^d$; each particle dies with rate 1 and generates a new particle at a randomly chosen neighboring vertex with rate $λ$, provided the chosen vertex is empty. Additionally, particles move according to a symmetric exclusion process with rate $N$. For any $d$ and $N$, there exists $λ_c$ such that, when the system starts from a single particle, particles go extinct when $λ< λ_c$ and have a chance of being present for all times when $λ> λ_c$. Durrett and Neuhauser proved that $λ_c$ …

Non-equilibrium Fluctuations of the Weakly Asymmetric Normalized Binary Contact Path Process

This paper is a further investigation of the problem studied in \cite{xue2020hydrodynamics}, where the authors proved a law of large numbers for the empirical measure of the weakly asymmetric normalized binary contact path process on $\mathbb{Z}^d,\, d \geq 3$, and then conjectured that a central limit theorem should hold under a non-equilibrium initial condition. We prove that the aforesaid conjecture is true when the dimension $d$ of the underlying lattice and the infection rate $λ$ of the process are sufficiently large.

A stochastic comparison result for the multitype contact process with unequal death rates

A stochastic comparison result that makes progress towards understanding the classical multitype contact process with unequal death rates is given. It has long been conjectured that the particle type with the largest birth to death rate ratio survives and the other dies out. A point process coupling result of Broman is used to give a sufficient condition for when the dominant particle type survives.

关于 Alzer-Berg 问题：一个最优 Bernstein 边界与唯一性猜想

On the Alzer-Berg problem: an optimal Bernstein boundary and a uniqueness conjecture

针对 Alzer-Berg 完全单调性问题，通过正性传递不等式与卷积恒等式刻画了最优 Bernstein 边界，并提出了边界点唯一性与二次接触的猜想。

Exponential growth and continuous phase transitions for the contact process on trees

We study the supercritical contact process on Galton-Watson trees and periodic trees. We prove that if the contact process survives weakly then it dominates a supercritical Crump-Mode-Jagers branching process. Hence the number of infected sites grows exponentially fast. As a consequence we conclude that the contact process dies out at the critical value $λ_1$ for weak survival, and the survival probability $p(λ)$ is continuous with respect to the infection rate $λ$. Applying this fact, we show the contact process on a general periodic tree experiences two phase transitions in the sense that $λ…