Related papers: Asymptotic expansion of the multi-orientable rando…
I compute several terms of the asymptotic expansion of the number of connected labelled graphs with n nodes and m edges, for small k=m-n.
Many enumeration problems in combinatorics, including such fundamental questions as the number of regular graphs, can be expressed as high-dimensional complex integrals. Motivated by the need for a systematic study of the asymptotic…
A Gelfand-Tsetlin scheme of depth N is a triangular array with m integers at level m, m=1,...,N, subject to certain interlacing constraints. We study the ensemble of uniformly random Gelfand-Tsetlin schemes with arbitrary fixed N-th row. We…
We study solutions of three-term recurrence relations whose $N$-step transfer matrices belong to the uniform Stolz class. In particular, we derive the first order of their uniform asymptotics. For orthonormal polynomials we show more.…
In order to deal with multidimensional structure representations of real-world networks, as well as with their worst-case irreducible information content analysis, the demand for new graph abstractions increases. This article investigates…
Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies…
We examine the asymptotic expansion of the Touchard polynomials $T_n(z)$ (also known as the exponential polynomials) for large $n$ and complex values of the variable $z$. In our treatment $|z|$ may be finite or allowed to be large like…
We initiate the study of limit shapes for random permutations avoiding a given pattern. Specifically, for patterns of length 3, we obtain delicate results on the asymptotics of distributions of positions of numbers in the permutations. We…
The purpose of this paper is to outline a generalised model for representing hybrids of relational-categorical, symbolic, perceptual-sensory and perceptual-latent data, so as to embody, in the same architectural data layer, representations…
We give simple criteria to identify the exponential order of magnitude of the absolute value of the determinant for wide classes of random matrix models, not requiring the assumption of invariance. These include Gaussian matrices with…
The exponential family of random graphs has been a topic of continued research interest. Despite the relative simplicity, these models capture a variety of interesting features displayed by large-scale networks and allow us to better…
In this paper, we study a multidimensional risk model with a common renewal process and in the presence of a constant interest force. The claim sizes are independent and identically distributed random vectors, with the distribution of…
We study asymmetric rank-one spiked tensor models in the high-dimensional regime, where the noise entries are independent and identically distributed with zero mean, unit variance, and finite fourth moment. This extends the classical…
In this article we discuss estimation of the common variance of several normal populations with tree order restricted means. We discuss the asymptotic properties of the maximum likelihood estimator of the variance as the number of…
Invariant tensors are states in the (local) SU(2) tensor product representation but invariant under global SU(2) action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An…
In this paper, we study the structure of the complete asymptotic expansion of the probability that a large combinatorial object is connected or consists of a given number of connected components. For rapidly growing labeled families of…
Consider a family $\mathcal{T}$ of 3-connected graphs of moderate growth, and let $\mathcal{G}$ be the class of graphs whose 3-connected components are graphs in $\mathcal{T}$. We present a general framework for analyzing such graphs…
Regular and singular parts of asymptotic expansions of semi-Markov random evolutions are given. Regularity of boundary conditions is shown. An algorithm for calculation of initial conditions is proposed.
The goal of this note is to provide a recursive algorithm that allows one to calculate the expansion of the metric tensor up to the desired order in Riemann normal coordinates. We test our expressions up to fourth order and predict results…
In this paper, we establish the first and the second-order asymptotics of distributions of normalized maxima of independent and non-identically distributed bivariate Gaussian triangular arrays, where each vector of the $n$th row follows…