相关论文: Volume growth and heat kernel estimates for the co…
We study a natural analogue of Ulam's problem for random rooted trees distributed according to a Plancherel-type measure. This probability measure is closely related to the classical Plancherel measure on integer partitions. For a…
We construct near-optimal coresets for kernel density estimates for points in $\mathbb{R}^d$ when the kernel is positive definite. Specifically we show a polynomial time construction for a coreset of size $O(\sqrt{d}/\varepsilon\cdot…
In this paper, we study the transition densities of pure-jump symmetric Markov processes in $ {{\mathbb R}}^d$, whose jumping kernels are comparable to radially symmetric functions with mixed polynomial growths. Under some mild assumptions…
We study first order fluctuations of a relativistic membrane in the curved background of a black hole. The zeroth-order solution corresponds to a spherical membrane tightly covering the event horizon. We obtain a massive Klein-Gordon…
We study random skew 3D partitions weighted by $q^{\textup{vol}}$ and, specifically, the $q\to 1$ asymptotics of local correlations near various points of the limit shape. We obtain sine-kernel asymptotics for correlations in the bulk of…
We study Bernoulli bond percolation on a random recursive tree of size $n$ with percolation parameter $p(n)$ converging to $1$ as $n$ tends to infinity. The sizes of the percolation clusters are naturally stored in a tree. We prove…
In this paper we prove a sharpened asymptotic for the growth of analytic torsion of congruence quotients of $\SL(n,\R)/\SO(n)$ in terms of the volume. The result is based on bounds on the trace of the heat kernel, allowing control of the…
In standard nucleation theory, the nucleation process is characterized by computing $\Delta\Omega(V)$, the reversible work required to form a cluster of volume $V$ of the stable phase inside the metastable mother phase. However, other…
A functorial derivation is presented of a heat-kernel expansion coefficient on a manifold with a singular fixed point set of codimension two. The existence of an extrinsic curvature term is pointed out.
This paper delineates the first steps in a systematic quantitative study of the spacetime fluctuations induced by quantum fields in an evaporating black hole under the stochastic gravity program. The central object of interest is the noise…
As a fundamental measure of stability in nonequilibrium thermodynamics, fluctuations provide critical insight into the performance and reliability of heat engines. In this work, we establish universal fluctuation-dissipation bounds that…
This paper is concerned about random walks on random environments in the lattice $\mathbb{Z}^d$. This model is analyzed through ergodicity in the form of the logarithmic Sobolev inequality. We assume that the environments are random…
We consider polynomial Bergman kernels with respect to exponentially varying weights $e^{-n \mathscr Q(z)}$ depending on a potential $\mathscr Q:\mathbb C^d\to\mathbb R$. We use these kernels to construct determinantal point processes on…
We investigate the possibility of statistical explanation of the black hole entropy by counting quasi-bounded modes of thermal fluctuation in two dimensional black hole spacetime. The black hole concerned is quantum in the sense that it is…
In this paper, we prove optimal local universality for roots of random polynomials with arbitrary coeffcients of polynomial growth. As an application, we derive, for the first time, sharp estimates for the number of real roots of these…
The quantization of gauge fields and gravitation on manifolds with boundary makes it necessary to study boundary conditions which involve both normal and tangential derivatives of the quantized field. The resulting one-loop divergences can…
The local limit theorem describes the behavior of the convolution powers of a probability distribution supported on Z. In this work, we explore the role played by positivity in this classical result and study the convolution powers of the…
Three-dimensional icosahedral random tilings with rhombohedral cells are studied in the semi-entropic model. We introduce a global energy measure defined by the variance of the quasilattice points in the orthogonal space. The internal…
In this paper, sharp two-sided estimates for the transition densities of relativistic $\alpha$-stable processes with mass $m\in (0, 1]$ in $C^{1,1}$ exterior open sets are established for all time $t>0$. These transition densities are also…
The mean square fluctuation and the expectation value of the stress-energy-momentum tensor of a neutral massive scalar field at finite temperature are determined near an infinite plane Dirichlet wall, and also near an infinite plane Neumann…