相关论文: A phase transition in the Bakry-\'Emery gradient e…
The aim of the present paper is to bridge the gap between the Bakry-\'{E}mery and the Lott-Sturm-Villani approaches to provide synthetic and abstract notions of lower Ricci curvature bounds. We start from a strongly local Dirichlet form…
We derive rates of convergence for limit theorems that reveal the intricate structure of the phase transitions in a mean-field version of the Blume-Emery-Griffith model. The theorems consist of scaling limits for the total spin. The model…
We construct a strongly local symmetric Dirichlet form on the configuration space $\Upsilon$ whose symmetrising (thus also invariant) measure is $\mathsf{sine}_\beta$, which is the law of the sine $\beta$ ensemble for every $\beta>0$. For…
Gradient bounds had proved to be a very efficient tool for the control of the rate of convergence to equilibrium for parabolic evolution equations. Among the gradient bounds methods, the celebrated Bakry-\'Emery criterion is a powerful way…
For general $\beta \geq 1$, we consider Dyson Brownian motion at equilibrium and prove convergence of the extremal particles to an ensemble of continuous sample paths in the limit $N \to \infty$. For each fixed time, this ensemble is…
The Bakry-Emery generalized Ricci tensor arises in scalar-tensor gravitation theories in the conformal gauge known as the Jordan frame. Recent results from the mathematics literature show that standard singularity and splitting theorems…
We characterize lower bounds for the Bakry-Emery Ricci tensor of nonsymmetric diffusion operators by convexity of entropy on the $L^2$-Wasserstein space, and define a curvature-dimension condition for general metric measure spaces together…
In this paper, a comprehensive examination of the temperature- and bias-dependent diffusion regimes of underdamped Brownian particles is presented. A temperature threshold for a transition between anomalous and normal diffusive behaviors is…
In this work, the quantum phase transition in the sub-Ohmic spin-boson model is studied using a single-mode approximation, by combining the rotating wave transformation and the transformations used in the numerical renormalization group…
We prove that the Dirichlet forms associated with the unlabelled infinite Dyson Brownian motion with the inverse temperature $\beta=2$ do not have a spectral gap.
In this paper, we study the edge behavior of Dyson Brownian motion with general $\beta$. Specifically, we consider the scenario where the averaged initial density near the edge, on the scale $\eta_*$, is lower bounded by a square root…
Reflected Brownian motion (RBM) in a wedge is a 2-dimensional stochastic process Z whose state space in R^2 is given in polar coordinates by S={(r,theta): r >= 0, 0 <= theta <= xi} for some 0 < xi < 2 pi. Let alpha= (theta_1+theta_2)/xi,…
We construct Dyson Brownian motion for $\beta \in (0,\infty]$ by adapting the extrinsic construction of Brownian motion on Riemannian manifolds to the geometry of group orbits within the space of Hermitian matrices. When $\beta$ is…
One-dimensional system of Brownian motions called Dyson's model is the particle system with long-range repulsive forces acting between any pair of particles, where the strength of force is $\beta/2$ times the inverse of particle distance.…
Consider the first exit time of one-dimensional Brownian motion $\{B_s\}_{s\geq 0}$ from a random passageway. We discuss a Brownian motion with two time-dependent random boundaries in quenched sense. Let $\{W_s\}_{s\geq 0}$ be an other…
We study Poincar{\'e} inequalities and long-time behavior for diffusion processes on R^n under a variable curvature lower bound, in the sense of Bakry-Emery. We derive various estimates on the rate of convergence to equilibrium in L^1…
We review and study a one-parameter family of functional transformations, denoted by $(S^{(\beta)})_{\beta\in \R}$, which, in the case $\beta<0$, provides a path realization of bridges associated to the family of diffusion processes…
Circular Dyson Brownian motion describes the Brownian dynamics of particles on a circle (periodic boundary conditions), interacting through a logarithmic, long-range two-body potential. Within the log-gas picture of random matrix theory, it…
In this paper we prove mean curvature comparisons and volume comparisons on a smooth metric measure space when the integral radial Bakry-\'Emery Ricci tensor and the potential function or its gradient are bounded. As applications, we prove…
The boundary beta-function generates the renormalization group acting on the universality classes of one-dimensional quantum systems with boundary which are critical in the bulk but not critical at the boundary. We prove a gradient formula…