相关论文: Fluctuations of two-dimensional determinantal proc…
In the past decade there has been a flurry of activity at the intersection of spectral theory and symplectic geometry. In this paper we review recent results on semiclassical spectral theory for commuting Berezin-Toeplitz and…
We develop physically admissible lattice models in the harmonic approximation which define by Hamilton's variational principle fractional Laplacian matrices of the forms of power law matrix functions on the n -dimensional periodic and…
In this paper we consider a class of probability distributions on the six-vertex model from statistical mechanics, which originate from the higher spin vertex models of https://arxiv.org/abs/1601.05770. We define operators, inspired by the…
We investigate the asymptotic behaviour of networks of interacting non-linear Hawkes processes modeling a homogeneous population of neurons in the large population limit. In particular, we prove a functional central limit theorem for the…
Constraints can affect dramatically the behavior of diffusion processes. Recently, we analyzed a natural and a technological system and reported that they perform diffusion-like discrete steps displaying a peculiar constraint, whereby the…
We derive the non-equilibrium fluctuations of one-dimensional symmetric simple exclusion processes in contact with slowed stochastic reservoirs which are regulated by a factor $n^{-\theta}$. Depending on the range of $\theta$ we obtain…
We study the fluctuations of smooth linear statistics of Laplace eigenvalues of compact hyperbolic surfaces lying in short energy windows, when averaged over the moduli space of surfaces of a given genus. The average is taken with respect…
The abstract theory of self-adjoint extensions of symmetric operators is used to construct self-adjoint realizations of a second-order elliptic operator on $\mathbb{R}^{n}$ with linear boundary conditions on (a relatively open part of) a…
The conversion of resolvent conditions into semigroup estimates is crucial in the stability analysis of hyperbolic partial differential equations. For two families of multiple Toeplitz operators, we relate the power bound with a resolvent…
The effect of thermally generated bulk stochastic forces on the statistical growth dynamics of forwards bifurcating propagating macroscopic patterns is compared with the influence of fluctuations at the boundary of a semiinfinite system,…
In this article, we study strictly elliptic, second-order differential operators on a bounded Lipschitz domain in $\mathbb{R}^d$, subject to certain non-local Wentzell-Robin boundary conditions. We prove that such operators generate…
Motivated by the task of computing normalizing constants and importance sampling in high dimensions, we study the dimension dependence of fluctuations for additive functionals of time-inhomogeneous Langevin-type diffusions on…
In this paper, we propose a drift-diffusion process on the probability simplex to study stochastic fluctuations in probability spaces. We construct a counting process for linear detailed balanced chemical reactions with finite species such…
In this note, we prove that the Fourier-Laplace transform of the typical function (i.e., generic in the sense of Baire category theorem) in the Schwartz class of the half-line, being analytic in the lower half of the complex plane, has…
We consider Berezin-Toeplitz operators whose multipliers are compactly supported densities carried by a submanifold of ${\mathbb C}^N$ . We compute asymptotically the moments of their spectral measures, and we prove Szeg\"o limit theorems…
The orientation fluctuations of the director of a liquid crystal are measured, by a sensitive polarization interferometer, close to the Fr\'eedericksz transition, which is a second order transition driven by an electric field. We show that…
We prove a two-term asymptotic expansion of eigenvalue sums of the Laplacian on a bounded domain with Neumann, or more generally, Robin boundary conditions. We formulate and prove the asymptotics in terms of semi-classical analysis. In this…
We study the eigenvalues of the Dirichlet Laplace operator on an arbitrary bounded, open set in $\R^d$, $d \geq 2$. In particular, we derive upper bounds on Riesz means of order $\sigma \geq 3/2$, that improve the sharp Berezin inequality…
Our work deals with symmetric rational functions and probabilistic models based on the fully inhomogeneous six vertex (ice type) model satisfying the free fermion condition. Two families of symmetric rational functions $F_\lambda,G_\lambda$…
We consider the Symmetric Exclusion Process on a compact Riemannian manifold, as introduced in van Ginkel and Redig (2020). There it was shown that the hydrodynamic limit satisfies the heat equation. In this paper we study the equilibrium…