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In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…
Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null…
For integers $g,m \geq 0$ and $n>0$, let $S_{g}(n,m)$ denote the graph taken uniformly at random from the set of all graphs on $\{1,2, \ldots, n\}$ with exactly $m=m(n)$ edges and with genus at most $g$. We use counting arguments to…
We prove that all 'gradient span algorithms' have asymptotically deterministic behavior on scaled Gaussian random functions as the dimension tends to infinity. In particular, this result explains the counterintuitive phenomenon that…
We investigate the nonparametric, composite hypothesis testing problem for arbitrary unknown distributions in the asymptotic regime where both the sample size and the number of hypotheses grow exponentially large. Such asymptotic analysis…
Let $K_n$ be the convex hull of i.i.d. random variables distributed according to the standard normal distribution on $\R^d$. We establish variance asymptotics as $n \to \infty$ for the re-scaled intrinsic volumes and $k$-face functionals of…
We investigate the rate of convergence of the iterates of an n-dimensional quasiregular mapping within the basin of attraction of a fixed point of high local index. A key tool is a refinement of a result that gives bounds on the distortion…
We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its…
We consider infinite graph-directed iterated function systems (GIFSs) whose contraction mappings are nonconformal. As our main result, we formulate asymptotic perturbations from conformal GIFSs to nonconformal GIFSs, and give the asymptotic…
The goal of this paper is to develop methodology for the systematic analysis of asymptotic statistical properties of data driven DRO formulations based on their corresponding non-DRO counterparts. We illustrate our approach in various…
We consider the Halfin-Whitt diffusion process $X_d(t)$, which is used, for example, as an approximation to the $m$-server $M/M/m$ queue. We use recently obtained integral representations for the transient density $p(x,t)$ of this diffusion…
In this article, we study linearly edge-reinforced random walk on general multi-level ladders for large initial edge weights. For infinite ladders, we show that the process can be represented as a random walk in a random environment, given…
We consider a noninteracting disordered system designed to model particle diffusion, relaxation in glasses, and impurity bands of semiconductors. Disorder originates in the random spatial distribution of sites. We find strong numerical…
We explore the asymptotic behavior of the centroids of random polygons constructed from regular polygons with vertices on the unit circle by extending the rays so that their lengths form a random permutation of the first (n) integers.…
To each sequence $(a_n)$ of positive real numbers we associate a growing sequence $(T_n)$ of continuous trees built recursively by gluing at step $n$ a segment of length $a_n$ on a uniform point of the pre-existing tree, starting from a…
We analyse uniform random cubic rooted planar maps and obtain limiting distributions for several parameters of interest. From the enumerative point of view, we present a unified approach for the enumeration of several classes of cubic…
A weighted recursive tree is an evolving tree in which vertices are assigned random vertex-weights and new vertices connect to a predecessor with a probability proportional to its weight. Here, we study the maximum degree and near-maximum…
It is well known that many random graphs with infinite variance degrees are ultrasmall. More precisely, for configuration models and preferential attachment models where the proportion of vertices of degree at least $k$ is approximately…
A special type of geometric situation in ensembles of non-intersecting paths occurs when the non-intersecting trajectories are required to be nonnegative so that the limit shape becomes tangential to the hard-edge $0$. The local fluctuation…
In this paper we study the asymptotic of multiplicities of irreducible representations in large tensor products of finite dimensional representations of simple Lie algebras and their statistics with respect to Plancherel and character…