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We present a genus expansion-type expression for the expected values of products of traces of expressions involving Haar-distributed orthogonal matrices. As with other real genus expansions, nonorientable surfaces appear, in addition to the…

This paper presents asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators within a two-way crossed mixed effect model as the sizes of the rows, columns, and cells tend to infinity. Under very mild…

We consider the asymptotic distribution of a cell in a 2 x ... x 2 contingency table as the fixed marginal totals tend to infinity. The asymptotic order of the cell variance is derived and a useful diagnostic is given for determining…

This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of…

Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we…

The main contribution of this note is to establish a framework to extend results of tensor functions over specific field to general field. As a consequence of this framework, we extend the existing work to more general settings: \emph{(1)}…

Let P_{n,m} denote the graph taken uniformly at random from the set of all planar graphs on {1,2,..., n} with exactly m(n) edges. We use counting arguments to investigate the probability that P_{n,m} will contain given components and…

Computing the embedding distribution of a given graph is a fundamental question in topological graph theory. In this article, we extend our viewpoint to a sequence of graphs and consider their asymptotic embedding distributions, which are…

We describe the asymptotic properties of the edge-triangle exponential random graph model as the natural parameters diverge along straight lines. We show that as we continuously vary the slopes of these lines, a typical graph drawn from…

A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…

We investigate average gradient degree of normal random polynomials of fixed algebraic degree n. In particular, for polynomials of two variables, asymptotics of the average gradient degree for large values of n is determined.

We develop a new method for studying the asymptotics of symmetric polynomials of representation-theoretic origin as the number of variables tends to infinity. Several applications of our method are presented: We prove a number of theorems…

Matrix models with continuous symmetry are powerful tools for studying quantum gravity and holography. Tensor models have also found applications in holographic quantum gravity. Matrix models with discrete permutation symmetry have been…

We introduce a generalization of the O(N) field theory to N-colored membranes of arbitrary inner dimension D. The O(N) model is obtained for D->1, while N->0 leads to self-avoiding tethered membranes (as the O(N) model reduces to…

We establish limit theorems that describe the asymptotic local and global geometric behaviour of random enriched trees considered up to symmetry. We apply these general results to random unlabelled weighted rooted graphs and uniform random…

We study the distribution of the length of longest monotone subsequences in random (fixed-point free) involutions of $n$ integers as $n$ grows large, establishing asymptotic expansions in powers of $n^{-1/6}$ in the general case and in…

We demonstrate that random tensors transforming under rank-$5$ irreducible representations of $\mathrm{O}(N)$ can support melonic large $N$ expansions. Our construction is based on models with sextic ($5$-simplex) interaction, which…

We continue to investigate some classes of Szeg\"o type polynomials in several variables. We focus on asymptotic properties of these polynomials and we extend several classical results of G. Szeg\"o to this setting.

An asymptotic analytical approach is proposed for bosonic probability amplitudes in unitary linear networks, such as the optical multiport devices for photons. The asymptotic approach applies for large number of bosons $N\gg M$ in the…

We study quantum dichotomies and the resource theory of asymmetric distinguishability using a generalization of Strassen's theorem on preordered semirings. We find that an asymptotic variant of relative submajorization, defined on…