Related papers: A New Bound on the Cumulant Generating Function of…

A ``hybrid method'', dedicated to asymptotic coefficient extraction in combinatorial generating functions, is presented, which combines Darboux's method and singularity analysis theory. This hybrid method applies to functions that remain of…

We study the Dirichlet problem for the following prescribed mean curvature PDE $$ \begin{cases} -\operatorname{div}\dfrac{\nabla v}{\sqrt{1+|\nabla v|^{2}}}=f(x,v) \text{ in }\Omega\\ v=\varphi \text{ on }\partial\Omega. \end{cases} $$…

In this work, we study general Dirichlet coalescents, which are a family of Xi-coalecents constructed from i.i.d mass partitions, and are an extension of the symmetric coalescent. This class of models is motivated by population models with…

For a Markov process associated with a diffusion type Dirichlet form an upper bound is shown for the law of the finite dimensional distributions of the process. Under some more assumptions on the underlaying space this is also shown for the…

In this paper, we consider a multi-block generalized alternating direction method of multiplier (GADMM) algorithm for minimizing a linearly constrained separable nonconvex and possibly nonsmooth optimization problem. The GADMM generalizes…

We develop a relative boundary theory for actions of discrete groups on compact spaces and use it to derive rigidity results for reduced crossed products. For a discrete group $\Gamma$ acting on a compact space $X$ and a subgroup $H$, we…

We develop a local theory of lacunary Dirichlet series of the form $\sum\limits_{k=1}^{\infty}c_k\exp(-zg(k)), \Re(z)>0$ as $z$ approaches the boundary $i\RR$, under the assumption $g'\to\infty$ and further assumptions on $c_k$. These…

A mixed Dirichlet-Neumann problem is regularized with a family of singularly perturbed Neumann-Robin boundary problems, parametrized by $\varepsilon > 0$. Using an asymptotic development by Gamma-convergence, the asymptotic behavior of the…

We prove a result of existence of positive solutions of the Dirichlet problem for $-\Delta_p u=\mathrm{w}(x)f(u,\nabla u)$ in a bounded domain $\Omega\subset\mathbb{R}^N$, where $\Delta_p$ is the $p$-Laplacian and $\mathrm{w}$ is a weight…

We utilize the weak convergence method to establish the Freidlin--Wentzell large deviations principle (LDP) for stochastic delay differential equations (SDDEs) with super-linearly growing coefficients, which covers a large class of cases…

In this work, we analyse the metastability of non-reversible diffusion processes $$dX_t=\boldsymbol{b}(X_t)dt+\sqrt h\,dB_t$$ on a bounded domain $\Omega$ when $\mathbf{b}$ admits the decomposition $\mathbf{b}=-(\nabla f+\mathbf{\ell})$ and…

The goal of this paper is to solve a long standing open problem, namely, the asymptotic development of order $2$ by $\Gamma$-convergence of the mass-constrained Cahn-Hilliard functional. This is achieved by introducing a novel rearrangement…

This paper expands the Cyclic Block Proximal Gradient method for block separable composite minimization by allowing for inexactly computed gradients and proximal maps. The resultant algorithm, the Inexact Cyclic Block Proximal Gradient…

We prove a homogenization theorem for a class of quadratic convolution energies with random coefficients. Under suitably stated hypotheses of ergodicity and stationarity we prove that the $\Gamma$-limit of such energy is almost surely a…

We propose a new method for obtaining complete asymptotic expansions in a systematic manner, which is suitable for counting sequences of various graph families in dense regime. The core idea is to encode the two-dimensional array of…

For the multi-mode Dicke model in a transport setting that exhibits collective boson transmissions, we construct the equation of motion for the cumulant generating function. Approximating the exact system of equations at the level of…

In this paper we introduce a new approach for approximately counting in bounded degree systems with higher-order constraints. Our main result is an algorithm to approximately count the number of solutions to a CNF formula $\Phi$ when the…

An algorithm is proposed for determining asymptotics of the sum of a perturbative series in the strong coupling limit using given values of the expansion coefficients. Operation of the algorithm is illustrated by test examples, method for…

Let $\Omega$ be a bounded pseudoconvex domain in $\mathbb{C}^n$, and let $\phi$ be a strictly plurisubharmonic function on $\Omega$. For each $k\in\mathbb{N}$, we consider determinantal point process $\Lambda_k$ with kernel $K_{k\phi}$,…

In this paper we propose a model with a Dirichlet process mixture of gamma densities in the bulk part below threshold and a generalized Pareto density in the tail for extreme value estimation. The proposed model is simple and flexible…