Related papers: Asymptotic forms for hard and soft edge general $\…
We investigate the late-time asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws containing stiff relaxation terms. First, we introduce a Chapman-Enskog-type asymptotic expansion and derive an effective…
The vertices of the Cayley graph of a finitely generated semigroup form a set of sites which can be labeled by elements of a finite alphabet in a manner governed by a nonnegative real interaction matrix, respecting nearest neighbor…
We determine the leading order of the maximum of the random potential associated to a two-dimensional Coulomb gas for general $\beta$ and general confinement potential, extending the recent result of Lambert-Lebl\'e-Zeitouni. In the case…
In this paper we develop a gapless theory of BEC which can be applied to both trapped and homogeneous gases at zero and finite temperature. The many-body Hamiltonian for the system is written in a form which is approximately quadratic with…
The purpose of this paper is to provide a first class of explicit sufficient conditions for the central limit theorem and related results in the setup of non-uniformly (partially) expanding non iid random transformations, considered as…
Considered herein are the family of nonlinear equations with both dispersive and dissipative homogeneous terms appended. Solutions of these equations that start with finite energia decay to zero as time goes to infinity. We present an…
Many axiomatic definitions of entropy, such as the R\'enyi entropy, of a random variable are closely related to the $\ell_{\alpha}$-norm of its probability distribution. This study considers probability distributions on finite sets, and…
This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi…
Ram\'irez and Rider (2009) established that the hard edge of the spectrum of the $\beta$-Laguerre ensemble converges, in the high-dimensional limit, to the bottom of the spectrum of the stochastic Bessel operator. Using stochastic analysis…
The method of asymptotic expansions is used to build an approximation scheme relevant to celestial mechanics in relativistic theories of gravitation. A scalar theory is considered, both as a simple example and for its own sake. This theory…
In several recent publications Carlip, as well as Balachandran, Chandar and Momen, have proposed a statistical mechanical interpretation for black hole entropy in terms of ``would be gauge'' degrees of freedom that become dynamical on the…
We give overcrowding estimates for the Sine_beta process, the bulk point process limit of the Gaussian beta-ensemble. We show that the probability of having at least n points in a fixed interval is given by $e^{-\frac{\beta}{2} n^2…
Using universal predictions provided by classical soft theorems, we revisit the energy emission spectrum for gravitational scatterings of compact objects in the low-frequency expansion. We calculate this observable beyond the zero-frequency…
We develop non-asymptotically justified methods for hypothesis testing about the $p-$dimensional coefficients $\theta^{*}$ in (possibly nonlinear) regression models. Given a function $h:\,\mathbb{R}^{p}\mapsto\mathbb{R}^{m}$, we consider…
The $\mathfrak{osp}(2,N)$-BF formulation of dilaton supergravity in two dimensions is considered. We introduce a consistent class of asymptotic conditions preserved by the extended superreparametrization group of the thermal circle at…
This paper develops a general theory on rates of convergence of penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where the likelihood is interpreted in a broad sense that…
For statistical systems that violate one of the four Shannon-Khinchin axioms, entropy takes a more general form than the Boltzmann-Gibbs entropy. The framework of superstatistics allows one to formulate a maximum entropy principle with…
We derive sufficient conditions for a probability measure on a finite product space (a spin system) to satisfy a (modified) logarithmic Sobolev inequality. We establish these conditions for various examples, such as the (vertex-weighted)…
We study the soft covering phenomenon through the lens of Neyman--Pearson hypothesis testing: given a channel output sequence $y^n$, can one decide whether it was produced when the channel was driven by a random codeword, or generated…
We give sharp conditions for the large time asymptotic simplification of aggregation-diffusion equations with linear diffusion. As soon as the interaction potential is bounded and its first and second derivatives decay fast enough at…