Spectral gap estimates for interacting particle systems via a Bochner-type identity

图上的Bochner恒等式

Bochner's Identity on Graphs

本文在图上证明了类似于Riemannian流形上Bochner恒等式的恒等式，并引入完全切图这一辅助图来处理对应于Ricci曲率的项。

Entropy decay for interacting systems via the Bochner--Bakry--Emery approach

We obtain estimates on the exponential rate of decay of the relative entropy from equilibrium for Markov processes with a non-local infinitesimal generator. We adapt some of the ideas coming from the Bakry-Emery approach to this setting. In particular, we obtain volume-independent lower bounds for the Glauber dynamics of interacting point particles and for various classes of hardcore models.

Convex Entropy Decay via the Bochner-Bakry-Emery approach

We develop a method, based on a Bochner-type identity, to obtain estimates on the exponential rate of decay of the relative entropy from equilibrium of Markov processes in discrete settings. When this method applies the relative entropy decays in a convex way. The method is shown to be rather powerful when applied to a class of birth and death processes. We then consider other examples, including inhomogeneous zero-range processes and Bernoulli-Laplace models. For these two models, known results were limited to the homogeneous case, and obtained via the martingale approach, whose applicability…

Laplace operators in deRham complexes associated with measures on configuration spaces

Let $Γ_X$ denote the space of all locally finite configurations in a complete, stochastically complete, connected, oriented Riemannian manifold $X$, whose volume measure $m$ is infinite. In this paper, we construct and study spaces $L^2_μΩ^n$ of differential $n$-forms over $Γ_X$ that are square integrable with respect to a probability measure $μ$ on $Γ_X$. The measure $μ$ is supposed to satisfy the condition $Σ_m'$ (generalized Mecke identity) well known in the theory of point processes. On $L^2_μΩ^n$, we introduce bilinear forms of Bochner and deRham type. We prove their closabilty and call t…

Narayana数在“显式充分不变量用于相互作用粒子系统（由Itoh, Mallows, 和 Shepp提出）”中的应用

Narayana numbers in "explicit sufficient invariants for an interacting particle system ( by Itoh, Mallows, and Shepp)"

本文研究星图上的相互作用粒子系统，利用无限多个以Narayana数为系数的鞅不变量获取马尔可夫链的极限分布，并通过平面无标记树的枚举恒等式经变量替换求得死亡状态概率。

Cores of Dirichlet forms related to random matrix theory

We prove the sets of polynomials on configuration spaces are cores of Dirichlet forms describing interacting Brownian motion in infinite dimensions. Typical examples of these stochastic dynamics are Dyson's Brownian motion and Airy interacting Brownian motion. Both particle systems have logarithmic interaction potentials, and naturally arise from random matrix theory. The results of the present paper will be used in a forth coming paper to prove the identity of the infinite-dimensional stochastic dynamics related to the random matrix theories constructed by apparently different methods: the me…