Related papers: Left-right crossings in the Miller-Abrahams random…

We consider the interlacement Poisson point process on the space of doubly-infinite Z^d-valued trajectories modulo time-shift, tending to infinity at positive and negative infinite times. The set of vertices and edges visited by at least…

Uniform random intersection graphs have received much interest and been used in diverse applications. A uniform random intersection graph with $n$ nodes is constructed as follows: each node selects a set of $K_n$ different items uniformly…

There has been growing interest in studies of general random intersection graphs. In this paper, we consider a general random intersection graph $\mathbb{G}(n,\overrightarrow{a}, \overrightarrow{K_n},P_n)$ defined on a set $\mathcal{V}_n$…

The study of spectrum statistics, such as the consecutive-gap ratio distribution, has revealed many interesting properties of many-body complex systems. Here we propose a two-parameter surmise expression for such distribution to describe…

We consider two classes of random graphs: $(a)$ Poissonian random graphs in which the $n$ vertices in the graph have i.i.d.\ weights distributed as $X$, where $\mathbb{E}(X) = \mu$. Edges are added according to a product measure and the…

A fundamental problem in network data analysis is to test Erd\"{o}s-R\'{e}nyi model $\mathcal{G}\left(n,\frac{a+b}{2n}\right)$ versus a bisection stochastic block model $\mathcal{G}\left(n,\frac{a}{n},\frac{b}{n}\right)$, where $a,b>0$ are…

Consider a bipartite random geometric graph on the union of two independent homogeneous Poisson point processes in $d$-space, with distance parameter $r$ and intensities $\lambda,\mu$. We show for $d \geq 2$ that if $\lambda$ is…

We prove that the local limit of the weighted spanning trees on any simple connected high degree almost regular sequence of electric networks is the Poisson(1) branching process conditioned to survive forever, by generalizing [NP22] and…

We use the Stein-Chen method to obtain compound Poisson approximations for the distribution of the number of subgraphs in a generalised stochastic block model which are isomorphic to some fixed graph. This model generalises the classical…

The topic of this survey are geometric functionals of a Boolean model (in Euclidean space) governed by a stationary Poisson process of convex grains. The Boolean model is a fundamental benchmark of stochastic geometry and continuum…

In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…

Let $V$ be a set of $n$ vertices, ${\cal M}$ a set of $m$ labels, and let $\mathbf{R}$ be an $m \times n$ matrix of independent Bernoulli random variables with success probability $p$. A random instance $G(V,E,\mathbf{R}^T\mathbf{R})$ of…

Empty region graphs are graphs whose vertices are points in $\mathbb{R}^d$ and where two vertices are connected by an edge whenever some associated region does not contain any other vertices. We investigate the asymptotic behaviour of long…

We study Pippenger's model of Boolean networks with unreliable gates. In this model, the conditional probability that a particular gate fails, given the failure status of any subset of gates preceding it in the network, is bounded from…

We develop dependent hierarchical normalized random measures and apply them to dynamic topic modeling. The dependency arises via superposition, subsampling and point transition on the underlying Poisson processes of these measures. The…

We investigate the threshold $p_{\vec H}=p_{\vec H}(n)$ for the Ramsey-type property $G(n,p)\to \vec H$, where $G(n,p)$ is the binomial random graph and $G\to\vec H$ indicates that every orientation of the graph $G$ contains the oriented…

If $G$ is a graph and $\vec H$ is an oriented graph, we write $G\to \vec H$ to say that every orientation of the edges of $G$ contains $\vec H$ as a subdigraph. We consider the case in which $G=G(n,p)$, the binomial random graph. We…

Consider a stationary Poisson point process in $\mathbb{R}^d$ and connect any two points whenever their distance is less than or equal to a prescribed distance parameter. This construction gives rise to the well known random geometric…

Let $G$ be a connected and simply connected complex semisimple Lie group. For a collection of homogeneous $G$-spaces $G/Q$, we construct a finite atlas ${\mathcal{A}}_{\rm BS}(G/Q)$ on $G/Q$, called the Bott-Samelson atlas, and we prove…

Let $G$ be a connected complex semi-simple Lie group, and let $Z_{{\bf u}}$ be an $n$-dimensional Bott-Samelson variety of $G$, where ${\bf u}$ is any sequence of simple reflections in the Weyl group of $G$. We study the Poisson structure…