Related papers: Pickands-Piterbarg constants for self-similar Gaus…

We study here the random fluctuations in the number of critical points with values in an interval $I\subset \mathbb{R}$ for Gaussian spherical eigenfunctions $\left\{f_{\ell }\right\} $, in the high energy regime where $\ell \rightarrow…

We consider a two-dimensional analogue of Helmholtz resonator with walls of finite thickness in the critical case when there exists an eigenfrequency equalling to the limit of poles generated by both the bounded component of the resonator…

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

We consider a Wigner-type ensemble, i.e. large hermitian $N\times N$ random matrices $H=H^*$ with centered independent entries and with a general matrix of variances $S_{xy}=\mathbb E|H_{xy}|^2$. The norm of $H$ is asymptotically given by…

We consider the semiclassical operator $\hat{H}(\epsilon,h):=H_{0}(hD_{x})+\epsilon \tilde{P}_{0}$ on $L^{2}(\mathbb{R}^{l})$, where the symbol of $\hat{H}(\epsilon,h)$ corresponds to a perturbed classical Hamiltonian of the form:…

After reviewing the source-type solution of the Burgers equation with standard dissipativity, we study the hypoviscous counterpart of the Burgers equation. 1) We determine an equation that governs the near-identity transformation underlying…

The question is studied whether weak solutions of linear partial integrodifferential equations approach a constant spatial profile after rescaling, as time goes to infinity. The possible limits and corresponding scaling functions are…

This paper investigates the asymptotic behavior of the principal eigenvalue $\lambda(s)$, as $s\to+\infty$, for the following elliptic eigenvalue problem \begin{equation*}\label{E} -\Delta_{M}u-s\langle \nabla_M f, \nabla_M u\rangle_g +c…

Let $G$ be an $N \times N$ real matrix whose entries are independent identically distributed standard normal random variables $G_{ij} \sim \mathcal{N}(0,1)$. The eigenvalues of such matrices are known to form a two-component system…

In this paper, we establish the precise asymptotic behaviors of the tail probability and the transition density of a large class of isotropic L\'evy processes when the scaling order is between 0 and 2 including 2. We also obtain the precise…

We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics like the F function. For pairwise interaction processes we…

We study the Sobolev spaces $H^\sigma(K)$ and $H^\sigma_0(K)$ on p.c.f. self-similar sets in terms of the boundary behavior of functions. First, for $\sigma\in \mathbb{R}^+$, we make an exact description of the tangents of functions in…

We consider a random Hamiltonian $H:\Sigma\to\mathbb R$ defined on a compact space $\Sigma$ that admits a transitive action by a compact group $\mathcal G$. When the law of $H$ is $\mathcal G$-invariant, we show its expected free energy…

This paper investigates the classical Gurland ratio of the gamma function and introduces its modified form, $\mathcal{G}^{\star}(x,y)$, which is particularly amenable to analytic expansions. By utilizing the Weierstrass product…

This note gives a bound on the error of the leading term of the $t\to 0$ asymptotic expansion of the Hartman-Watson distribution $\theta(r,t)$ in the regime $rt=\rho$ constant. The leading order term has the form…

In this paper, we study the asymptotic behavior of solutions to a Gas-liquid model with external forces and general pressure law. Under some suitable assumptions on the initial date and $\gamma>1$, if…

The kinetic energy of a multi-particle system is described by the one-particle kinetic energy density matrix $\tau(x, y)$. Alongside the one-particle density matrix $\gamma(x, y)$, it is one of the key objects in the quantum-mechanical…

The limiting behavior of the eigenvalues of the Toeplitz matrices $T_{n}[\sigma]=(\hat{\sigma}(i-j))$, where $0\leq i,j \leq n$, as $n \to \infty$, is investigated in the case of complex valued functions $\sigma$ defined on the unit circle…

Let $\Phi^h(x)$ with $x=(t,y)$ denote the near-critical scaling limit of the planar Ising magnetization field. We take the limit of $\Phi^h$ as the spatial coordinate $y$ scales to infinity with $t$ fixed and prove that it is a stationary…

We study the intersection of two independent renewal processes, $\rho=\tau\cap\sigma$. Assuming that $\mathbf{P}(\tau_1 = n ) = \varphi(n)\, n^{-(1+\alpha)}$ and $\mathbf{P}(\sigma_1 = n ) = \tilde\varphi(n)\, n^{-(1+ \tilde\alpha)} $ for…