Related papers: Central limit theorem for the heat kernel measure …

We consider a general network of harmonic oscillators driven out of thermal equilibrium by coupling to several heat reservoirs at different temperatures. The action of the reservoirs is implemented by Langevin forces. Assuming the existence…

We establish a central limit theorem for counting large continued fraction digits $(a_n)$, i.e. we count occurrences $\{a_n>b_n\}$, where $(b_n)$ is a sequence of positive integers. Our result improves a similar result by Philipp which…

We analyze the full-counting statistics of the electric heat current flowing in a two-terminal quantum conductor whose temperature is probed by a third electrode ("probe electrode"). In particular we demonstrate that the cumulant-generating…

This work concerns the statistics of the Two-Time Measurement definition of heat variation in each reservoir of a thermodynamic quantum system. We study the cumulant generating function of the heat flows in the thermodynamic and large-time…

We consider the fluctuations of the number of eigenvalues of $n\times n$ random normal matrices depending on a potential $Q$ in a given set $A$. These eigenvalues are known to form a determinantal point process, and are known to accumulate…

We consider the empirical process G_t of a one-dimensional diffusion with finite speed measure, indexed by a collection of functions F. By the central limit theorem for diffusions, the finite-dimensional distributions of G_t converge weakly…

We prove Cameron-Martin type quasi-invariance results for the heat kernel measure of infinite-dimensional Kolmogorov and related diffusions. We first study quantitative functional inequalities for appropriate finite-dimensional…

We consider the empirical eigenvalue distribution of an $m\times m$ principle submatrix of an $n\times n$ random unitary matrix distributed according to Haar measure. Earlier work of Petz and R\'effy identified the limiting spectral measure…

We study the one-loop covariant effective action of Lifshitz theories using the heat kernel technique. The characteristic feature of Lifshitz theories is an anisotropic scaling between space and time. This is enforced by the existence of a…

A function on a discrete group is weakly combable if its discrete derivative with respect to a combing can be calculated by a finite state automaton. A weakly combable function is bicombable if it is Lipschitz in both the left and right…

We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices $W$ and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem…

A nonlinear generalization of the Fluctuation-Dissipation Theorem (FDT) for the n-point Green functions and the amputated 1PI vertex functions at finite temperature is derived in the framework of the Closed Time Path formalism. We verify…

This paper is an exposition of several questions linking heat kernel measures on infinite dimensional Lie groups, limits associated with critical Sobolev exponents, and Feynmann-Kac measures for sigma models.

We define an $f$-restricted partition $p_f(n,k)$ of fixed length $k$ given by the bivariate generating series \begin{align*} Q_f(z,u) \coloneqq 1+\sum_{n=1}^{\infty}\sum_{k=1}^{\infty} p_f(n,k) u^kz^n…

We study the large time behaviour of the reaction-diffsuion equation $\partial_t u=\Delta u +f(u)$ in spatial dimension $N$, when the nonlinear term is bistable and the initial datum is compactly supported. We prove the existence of a…

We consider the macroscopic large N limit of the Circular beta-Ensemble at high temperature, and its weighted version as well, in the regime where the inverse temperature scales as beta/N for some parameter beta>0. More precisely, in the…

We consider the system of $N$ one-dimensional free fermions confined by a harmonic well $V(x) = m\omega^2 {x^2}/{2}$ at finite inverse temperature $\beta = 1/T$. The average density of fermions $\rho_N(x,T)$ at position $x$ is derived. For…

In this article, we consider the problem of estimating the heat kernel on measure-metric spaces equipped with a resistance form. Such spaces admit a corresponding resistance metric that reflects the conductivity properties of the set. In…

Let $(Y_n)_n$ be a sequence of $\mathbb{R}^d$-valued random variables. Suppose that the generating function \[f(x, z) = \sum_{n = 0}^\infty \varphi_{Y_n}(x) z^n,\] where $\varphi_{Y_n}$ is the characteristic function of $Y_n$, extends to a…

Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite…