Related papers: High-dimensional Laplace asymptotics up to the con…

For a complex variable $s$ and real parameters $a$ and $\lambda$ with $a>0$, let $\phi(s,a,\lambda)$ denote the Lerch zeta-function with a complex variable, $\phi^{\ast}(s,a,\lambda)$ a slight modification of $\phi(s,a,\lambda)$ defined by…

Let $I_1=[a_0,a_1),\ldots,I_{k}= [a_{k-1},a_k)$ be a partition of the interval $I=[0,1)$ into $k$ subintervals. Let $f:I\to I$ be a map such that each restriction $f|_{I_i}$ is an increasing Lipschitz contraction. We prove that any $f$…

This paper extends the inductive approach to the lace expansion of van der Hofstad and Slade in order to prove Gaussian asymptotic behaviour for models with critical dimension other than 4. The results are applied by Holmes to study…

We study the asymptotic behavior of linear evolution equations of the type \partial_t g = Dg + Lg - \lambda g, where L is the fragmentation operator, D is a differential operator, and {\lambda} is the largest eigenvalue of the operator Dg +…

The purpose of this article is to describe the singularities of one-dimensional oscillatory integrals, whose phases have a certain singularity, in the form of an asymptotic expansion. In the case of the Laplace integral, an analogous result…

Boundary value problems for diffusion in singularly perturbed domains (domains with small holes removed from the interior) is a topic of considerable current interest. Applications include intracellular diffusive transport and the spread of…

In this work we establish under certain hypotheses the $N \to +\infty$ asymptotic expansion of integrals of the form $$\mathcal{Z}_{N,\Gamma}[V] \, = \, \int_{\Gamma^N} \prod_{ a < b}^{N}(z_a - z_b)^\beta \, \prod_{k=1}^{N} \mathrm{e}^{ - N…

We derive the first exact, rigorous but practical, globally valid remainder terms for asymptotic expansions about saddles and contour endpoints of arbitrary order degeneracy derived from the method of steepest descents. The exact remainder…

We prove optimal concentration of measure for lifted functions on high dimensional expanders (HDX). Let $X$ be a $k$-dimensional HDX. We show for any $i\leq k$ and $f:X(i)\to [0,1]$: \[\Pr_{s\in X(k)}\left[\left|\underset{{t\subseteq…

We establish a rigorous asymptotic theory for the joint estimation of roughness and scale parameters in two-dimensional Gaussian random fields with power-law generalized covariances \cite{Matheron1973, Stein1999, Yaglom1987}. Our main…

For a standard path of connections going to a generic point at infinity in the moduli space $M_{DR}$ of connections on a compact Riemann surface, we show that the Laplace transform of the family of monodromy matrices has an analytic…

Let (lambda_d)(p) be the p monomer-dimer entropy on the d-dimensional integer lattice Z^d, where p in [0,1] is the dimer density. We give upper and lower bounds for (lambda_d)(p) in terms of expressions involving (lambda_(d-1))(q). The…

Intrinsic volumes are fundamental geometric invariants generalizing volume, surface area, and mean width for convex bodies. We establish a unified Laplace-Grassmannian representation for intrinsic and dual volumes of convex polynomial…

We give an explicit description of the full asymptotic expansion of the Schwartz kernel of the complex powers of $m$-Laplace type operators $L$ on compact Riemannian manifolds in terms of Riesz distributions. The constant term in this…

In this paper, we study the extreme statistics in the complex Ginibre ensemble of $N \times N$ random matrices with complex Gaussian entries, but with no other symmetries. All the $N$ eigenvalues are complex random variables and their joint…

This paper provides several illustrations of the numerous remarkable properties of the lambda-extensions of the two-point correlation functions of the Ising model, sheding some light on the non-linear ODEs of the Painlev\'e type. We first…

Let $g_0$ be a smooth pinched negatively curved Riemannian metric on a complete surface $N$, and let $\Lambda_0$ be a basic hyperbolic set of the geodesic flow of $g_0$ with Hausdorff dimension strictly smaller than two. Given a small…

The paper is concerned with higher order Calderon-Zygmund estimates for the $p$-Laplace equation $$ -\textrm{div}(A(\nabla u)) := -\textrm{div}{(|\nabla u|^{p-2}\nabla u)}=-\textrm{div} F, \qquad 1<p<\infty. $$ We are able to transfer local…

Bayesian inference on non-Gaussian data is often non-analytic and requires computationally expensive approximations such as sampling or variational inference. We propose an approximate inference framework primarily designed to be…

We propose an inexact proximal augmented Lagrangian framework with explicit inner problem termination rule for composite convex optimization problems. We consider arbitrary linearly convergent inner solver including in particular stochastic…