Related papers: Effective Asymptotics of Combinatorial Systems
We define a type of generalized asymptotic series called $v$-asymptotic. We show that every function with moderate growth at infinity has a $v$-asymptotic expansion. We also describe the set of $v$-asymptotic series, where a given function…
The analytic and formal solutions to a family of singularly perturbed partial differential equations in the complex domain involving two complex time variables are considered. The analytic continuation properties of the solution of an…
We consider a finite collection of reinforced stochastic processes with a general network-based interaction among them. We provide sufficient and necessary conditions in order to have some form of almost sure asymptotic synchronization,…
Arithmetic combinatorics is often concerned with the problem of bounding the behaviour of arbitrary finite sets in a group or ring with respect to arithmetic operations such as addition or multiplication. Similarly, combinatorial geometry…
We develop an analytic theory of operator-valued additive free convolution in terms of subordination functions. In contrast to earlier investigations our functions are not just given by power series expansions, but are defined as Frechet…
In this document we achieve exact and asymptotic enumeration of words, compositions over a finite group, and/or integer compositions characterized by local restrictions and, separately, subsequence pattern avoidance. We also count…
Asymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given…
The generating function of the cumulants in random matrix models, as well as the cumulants themselves, can be expanded as asymptotic (divergent) series indexed by maps. While at fixed genus the sums over maps converge, the sums over genera…
We prove a general large sieve statement in the context of random walks on subgraphs of a given graph. This can be seen as a generalization of previously known results where one performs a random walk on a group enjoying a strong spectral…
We construct a new type of convergent asymptotic representations, dyadic factorial expansions. Their convergence is geometric and the region of convergence can include Stokes rays, and often extends down to 0^+. For special functions such…
We study Fibonacci compositions, which are compositions of natural numbers that only use Fibonacci numbers, in two different contexts. We first prove inequalities comparing the number of Fibonacci compositions to regular compositions where…
In this paper we apply techniques from nonstandard analysis to study expansive dynamical systems. Among other results, we provide a necessary and sufficient condition for an expansive homeomorphism on a compact metric space to admit…
The study of images of noncommutative polynomials on algebras has attracted considerable attention. We investigate polynomial images and the additive structures they generate in associative algebras, focusing on sums and products of values.…
We establish formulae for the asymptotic growth (with respect to the scaling dimension) of the number of operators in effective field theory, or equivalently the number of $S$-matrix elements, in arbitrary spacetime dimensions and with…
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
We prove an Asymptotic Implicit Function Theorem in the setting of Gevrey asymptotics with respect to a parameter. The unique implicitly defined solution admits a Gevrey asymptotic expansion and furthermore it is the Borel resummation of…
We study the asymptotic behavior, as time t goes to infinity, of nonautonomous dynamical systems involving multiscale features. These systems model the emergence of various collective behaviors in game theory, as well as the asymptotic…
In these lectures three different methods of computing the asymptotic expansion of a Hermitian matrix integral is presented. The first one is a combinatorial method using Feynman diagrams. This leads us to the generating function of the…
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…
Combinatorial Exploration is a new domain-agnostic algorithmic framework to automatically and rigorously study the structure of combinatorial objects and derive their counting sequences and generating functions. We describe how it works and…