Related papers: An edge CLT for the log determinant of Laguerre be…

Stochastic Loewner Evolution (SLE_kappa) has been introduced as a description of the continuum limit of cluster boundaries in two-dimensional critical systems. We show that the problem of N radial SLEs in the unit disc is equivalent to…

In this paper, we consider Muttalib-Borodin ensemble of Laguerre type, a determinantal point process over $[0,\infty)$ which depends on the varying weights $x^{\alpha}e^{-nV(x)}$, $\alpha>-1$, and a parameter $\theta$. For $\theta$ being a…

We argue that energetic muon-electron scattering in the backward direction can be viewed as a template case to study the resummation of large logarithms related to endpoint divergences appearing in the effective-theory formulation of…

In this paper, we study the Exponential Random Graph Models (ERGMs) conditioning on the number of edges. In subcritical region of model parameters, we prove a conditional Central Limit Theorem (CLT) with explicit mean and variance for the…

In this article, we revisit the question of fluctuations of linear statistics of beta ensembles in the single cut and non-critical regime for general potentials $V$ under mild regularity and growth assumptions. Our main objective is to…

Let $(\tau_n)$ be a sequence of toral automorphisms $\tau_n : x \rightarrow A_n x \hbox{mod}\ZZ^d$ with $A_n \in {\cal A}$, where ${\cal A}$ is a finite set of matrices in $SL(d, \mathbb{Z})$. Under some conditions the method of…

Under the Kolmogorov--Smirnov metric, an upper bound on the rate of convergence to the Gaussian distribution is obtained for linear statistics of the matrix ensembles in the case of the Gaussian, Laguerre, and Jacobi weights. The main lemma…

We consider the determinantal point processes associated with the spectral projectors of a Schr\"odinger operator on $\mathbb{R}$, with a smooth confining potential. In the semiclassical limit, where the number of particles tends to…

We study the central limit theorem (CLT) for linear eigenvalue statistics of several types of matrix models, whose entries are having exploding moments, i.e., moments of the entries are increasing with the size of the matrix. In particular,…

It is proved that for infinitely many positive integers n, there exists a circulant graph of order n whose Weisfeiler-Leman dimension is at least c\sqrt{log n} for some positive constant c not depending on n.

Using Bernstein polynomial approximations, we prove the central limit theorem for linear spectral statistics of sample covariance matrices, indexed by a set of functions with continuous fourth order derivatives on an open interval including…

$N$-dimensional Bessel and Jacobi processes describe interacting particle systems with $N$ particles and are related to $\beta$-Hermite, $\beta$-Laguerre, and $\beta$-Jacobi ensembles. For fixed $N$ there exist associated weak limit…

Consider the Ising model on $([1,2N]\times[1,2M])\cap\mathbb{Z}^2$ at critical temperature with periodic boundary condition in the horizontal direction and free boundary condition in the vertical direction. Let $E_{M,N}$ be its total energy…

We prove the Central Limit Theorem for the number of eigenvalues near the spectrum edge for hermitian ensembles of random matrices. To derive our results, we use a general theorem, essentially due to Costin and Lebowitz, concerning the…

Stochastic differential equations (SDEs) without global Lipschitz drift often demonstrate unusual phenomena. In this paper, we consider the following SDE on $\mathbb R^d$: \begin{align*} \mathrm{d} \mathbf{X}_t=\mathbf{b}(\mathbf{X}_t)…

The question of whether the central limit theorem (CLT) holds for the total number of edges in exponential random graph models (ERGMs) in the subcritical region of parameters has remained an open problem. In this paper, we establish the…

We present a new method to search for a light scalar top with $m_{\tilde{t}_1}\lsim m_t$, decaying dominantly into a c-jet and the lightest neutralino, at the LHC. The principal idea is to exploit the Majorana nature of the gluino, leading…

We use martingale embeddings to prove a central limit theorem (CLT) for one-dimensional projections of high-dimensional random vectors in $\{-1,1\}^n$ satisfying a Poincar\'e inequality. We obtain a non-asymptotic error bound involving…

We consider two $n\times n$ non-Hermitian random matrices such that the $ij$th entry of one matrix is correlated with the $ij$th entry of the other matrix. However, the entries of any particular matrix are i.i.d. random variables. We study…

We study the spectrum and OPE coefficients of the three-dimensional critical O(2) model, using four-point functions of the leading scalars with charges 0, 1, and 2 ($s$, $\phi$, and $t$). We obtain numerical predictions for low-twist OPE…