Related papers: Large deviations and renormalization for Riesz pot…
We consider the classical obstacle problem on bounded, connected Lipschitz domains $D \subset \mathbb{R}^n$. We derive quantitative bounds on the changes to contact sets under general perturbations to both the right hand side and the…
Let S_1(n),...,S_p(n) be independent symmetric random walks in Z^d. We establish moderate deviations and law of the iterated logarithm for the intersection of the ranges #{S_1[0,n]\cap... \cap S_p[0,n]} in the case d=2, p\ge 2 and the case…
We investigate the thermodynamic limit of the circular long-range Riesz gas, a system of particles interacting pairwise through an inverse power kernel. We show that after rescaling, so that the typical spacing of particles is of order $1$,…
Following Selberg it is known that uniformly for V << (logloglog T)^{1/2 - \epsilon} the measure of those t \in [T;2T] for which log |\zeta(1/2 + it)| > V*((1/2)loglog T)^{1/2} is approximately T times the probability that a standard…
Density matrix renormalization group (DMRG) is applied to a (1+1)-dimensional $\lambda\phi^4$ model to study spontaneous breakdown of discrete $Z_2$ symmetry numerically. We obtain the critical coupling $(\lambda/\mu^2)_{\rm c}=59.89\pm…
We consider a two-dimensional Hamiltonian system perturbed by a small diffusion term, whose coefficient is state-dependent and non-degenerate. As a result, the process consists of the fast motion along the level curves and slow motion…
The robust statistical description of dynamical systems under perturbations is a central problem in ergodic theory. In this paper, we investigate the statistical properties of skew-product maps driven by a subshift of finite type with…
The Sine-Gordon model is obtained by tilting the law of a log-correlated Gaussian field $X$ defined on a subset of $\mathbb{R}^d$ by the exponential of its cosine, namely $\exp(\alpha \smallint \cos (\beta X))$. It is an important model in…
The experimental determination of the partial width $\Gamma (H \longrightarrow \gamma \gamma)$ of an intermediate mass Higgs is among the most important measurements at a future photon photon collider. Recently it was shown that large…
We present a path integral calculation of the probability distribution associated with the time-integrated moments of the Ornstein-Uhlenbeck process that includes the Gaussian prefactor in addition to the dominant path or instanton term…
In this article we consider Wigner matrices $X_N$ with variance profiles (also called Wigner-type matrices) which are of the form $X_N(i,j) = \sigma(i/N,j/N) a_{i,j} / \sqrt{N}$ where $\sigma$ is a symmetric real positive function of…
Let L be a positive line bundle over a projective complex manifold X. Consider the space of holomorphic sections of the tensor power of order p of L. The determinant of a basis of this space, together with some given probability measure on…
We study a random configuration of $N$ soliton solutions $\psi_N(x,t;\boldsymbol{\lambda})$ of the cubic focusing Nonlinear Schr\"odinger (fNLS) equation in one space dimension. The $N$ soliton solutions are parametrized by $2N$ complex…
Homogeneous normalized random measures with independent increments (hNRMIs) represent a broad class of Bayesian nonparametric priors and thus are widely used. In this paper, we obtain the strong law of large numbers, the central limit…
The Dirichlet form associated with the intrinsic gradient on Poisson space is known to be quasi-regular on the complete metric space $\ddot\Gamma=$ $\{Z_+$-valued Radon measures on $\IR^d\}$. We show that under mild conditions, the set…
We prove mod-Gaussian convergence for a Dirichlet polynomial which approximates $\operatorname{Im}\log\zeta(1/2+it)$. This Dirichlet polynomial is sufficiently long to deduce Selberg's central limit theorem with an explicit error term.…
We study the normalized eigenvalue counting measure d\sigma of matrices of long-range percolation model. These are (2n+1)\times (2n+1) random real symmetric matrices H=\{H(i,j)\}_{i,j} whose elements are independent random variables taking…
Gaussian Multiplicative Chaos (GMC) is informally defined as a random measure $e^{\gamma X} \mathrm{d} x$ where $X$ is Gaussian field on $\mathbb R^d$ (or an open subset of it) whose correlation function is of the form $ K(x,y)= \log…
What does an Erdos-Renyi graph look like when a rare event happens? This paper answers this question when p is fixed and n tends to infinity by establishing a large deviation principle under an appropriate topology. The formulation and…
Let $S(\sigma,t)=\frac{1}{\pi}\arg\zeta(\sigma+it)$ be the argument of the Riemann zeta-function at the point $\sigma+it$ in the critical strip. For $n\geq 1$ and $t>0$, we define \begin{equation*} S_{n}(\sigma,t) = \int_0^t…