Related papers: Asymptotic Distribution of Eigenvalues for a Self-…
Let $f=(f_1,\ldots,f_n)$ be a system of $n$ complex homogeneous polynomials in $n$ variables of degree $d$. We call $\lambda\in\mathbb{C}$ an eigenvalue of $f$ if there exists $v\in\mathbb{C}^n\backslash\{0\}$ with $f(v)=\lambda v$,…
This paper investigates the asymptotic nature of graph spectra when some edges of a graph are subdivided sufficiently many times. In the special case where all edges of a graph are subdivided, we find the exact limits of the $k$-th largest…
We study the variance and the Laplace transform of the probability law of linear eigenvalue statistics of unitary invariant Matrix Models of n-dimentional Hermitian matrices as n tends to infinity. Assuming that the test function of…
We consider sequences of needlet random fields defined as weighted averaged forms of spherical Gaussian eigenfunctions. Our main result is a Central Limit Theorem in the high energy setting, for the boundary lengths of their excursion sets.…
Our aim in this paper is to investigate the asymptotic behavior of solutions of the perturbed linear fractional differential system. We show that if the original linear autonomous system is asymptotically stable then under the action of…
The spectral and localization properties of heterogeneous random graphs are determined by the resolvent distributional equations, which have so far resisted an analytic treatment. We solve analytically the resolvent equations of random…
We discuss the asymptotics of the eigenvalue counting function for partial differential operators and related expressions paying the most attention to the sharp asymptotics. We consider Weyl asymptotics, asymptotics with Weyl principal…
We study the spectrum of an invariant, elliptic, classical pseudodifferential operator on a closed G-manifold M, where G is a compact, connected Lie group acting effectively and isometrically on M. Using resolution of singularities, we…
Modularity is a popular metric for quantifying the degree of community structure within a network. The distribution of the largest eigenvalue of a network's edge weight or adjacency matrix is well studied and is frequently used as a…
At the classical level we study open bosonic strings. A generic description of string self-interactions localized at string ends is given. Self-interactions are characterized by two dimensionless coupling constants. The model is rewritten…
This paper studies the asymptotic distribution of a constrained lasso-type estimator for denoising signals defined on the nodes of a graph, where the underlying structure encodes relationships between variables. We show that, under suitable…
We show that an equilibriumlike additivity property can remarkably lead to power-law distributions observed frequently in a wide class of out-of-equilibrium systems. The additivity property can determine the full scaling form of the…
We develop an asymptotical control theory for one of the simplest distributed (infinite dimensional) oscillating systems, namely, for a closed string under a bounded load applied to a single distinguished point. We find exact classes of…
In this paper we derive some new and practical results on testing and interval estimation problems for the population eigenvalues of a Wishart matrix based on the asymptotic theory for block-wise infinite dispersion of the population…
Discrete random probability measures are a key ingredient of Bayesian nonparametric inferential procedures. A sample generates ties with positive probability and a fundamental object of both theoretical and applied interest is the…
We study the geometric distribution of the relative entropy of a charged localised state in Quantum Field Theory. With respect to translations, the second derivative of the vacuum relative entropy is zero out of the charge localisation…
Consider a random regular graph of fixed degree $d$ with $n$ vertices. We study spectral properties of the adjacency matrix and of random Schr\"odinger operators on such a graph as $n$ tends to infinity. We prove that the integrated density…
In this article, we provide a comprehensive analysis of the asymptotic behavior of Bell numbers, enhancing and unifying various results previously dispersed in the literature. We establish several explicit lower and upper bounds. The main…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
We revisit the problem of condensation for independent, identically distributed random variables with a power-law tail, conditioned by the value of their sum. For large values of the sum, and for a large number of summands, a condensation…