Related papers: On the easiest way to connect $k$ points in the Ra…

In this paper, we propose a paradigm for processing in parallel graph joins in road networks. The methodology we present can be used for distance join processing among the elements of two disjoint sets R,S of nodes from the road network,…

We consider the number of edge crossings in a random graph drawing generated by projecting a random geometric graph on some compact convex set $W\subset \mathbb{R}^d$, $d\geq 3$, onto a plane. The positions of these crossings form the…

Consider a countably infinite collection of interacting queues, with a queue located at each point of the $d$-dimensional integer grid, having independent Poisson arrivals, but dependent service rates. The service discipline is of the…

We derive large- and moderate-deviation results in random networks given as planar directed navigations on homogeneous Poisson point processes. In this non-Markovian routing scheme, starting from the origin, at each consecutive step a…

This paper derives normal approximation results for subgraph counts written as multiparameter stochastic integrals in a random-connection model based on a Poisson point process. By combinatorial arguments we express the cumulants of general…

For a given homogeneous Poisson point process in $\mathbb{R}^d$ two points are connected by an edge if their distance is bounded by a prescribed distance parameter. The behaviour of the resulting random graph, the Gilbert graph or random…

We consider simple random walks on random graphs embedded in $\mathbb{R}^d$ and generated by point processes such as Delaunay triangulations, Gabriel graphs and the creek-crossing graphs. Under suitable assumptions on the point process, we…

The Kolakoski sequence is the unique infinite sequence with values in $\{1,2\}$ and first term $1$ which equals the sequence of run-lengths of itself, we call this $K(1,2).$ We define $K(m,n)$ similarly. A well-known conjecture is that the…

We study random graphs, both $G(n,p)$ and $G(n,m)$, with random orientations on the edges. For three fixed distinct vertices s,a,b we study the correlation, in the combined probability space, of the events a -> s and s -> b. For G(n,p), we…

Let $\{X_i(t),t\ge0\}, 1\le i\le n$ be independent copies of a stationary process $\{X(t), t\ge0\}$. For given positive constants $u,T$, define the set of $r$th conjunctions $ C_{r,T,u}:= \{t\in [0,T]: X_{r:n}(t) > u\}$ with $X_{r:n}(t)$…

We consider random interlacements on $ \mathbb{Z}^d$, $d \ge 3$, when their vacant set is in a strongly percolative regime. Given a large box centered at the origin, we establish an asymptotic upper bound on the exponential rate of decay of…

We prove a Poisson limit theorem in the total variation distance of functionals of a general Poisson point process using the Malliavin-Stein method. Our estimates only involve first and second order difference operators and are closely…

A Poisson point process of unit intensity is placed in the square $[0,n]^2$. An increasing path is a curve connecting $(0,0)$ with $(n,n)$ which is non-decreasing in each coordinate. Its length is the number of points of the Poisson process…

Pick n points independently at random in R^2, according to a prescribed probability measure mu, and let D^n_1 <= D^n_2 <= ... be the areas of the binomial n choose 3 triangles thus formed, in non-decreasing order. If mu is absolutely…

We study the trajectory of a simple random walk on a d-regular graph with d>2 and locally tree-like structure as the number n of vertices grows. Examples of such graphs include random d-regular graphs and large girth expanders. For these…

The disjoint paths problem asks, given an graph G and k + 1 pairs of terminals (s_0,t_0), ...,(s_k,t_k), whether there are k+1 pairwise disjoint paths P_0, ...,P_k, such that P_i connects s_i to t_i. Robertson and Seymour have proven that…

We consider a variant of a classical coverage process, the boolean model in $\mathbb{R}^d$. Previous efforts have focused on convergence of the unoccupied region containing the origin to a well studied limit $C$. We study the intersection…

Consider a 2-dimensional soft random geometric graph $G(\lambda,s,\phi)$, obtained by placing a Poisson($\lambda s^2$) number of vertices uniformly at random in a square of side $s$, with edges placed between each pair $x,y$ of vertices…

A graph on at least ${{k+1}}$ vertices is uniformly $k$-connected if each pair of its vertices is connected by $k$ and not more than $k$ independent paths. We reinvestigate a recent constructive characterization of uniformly $3$-connected…

We find the asymptotic number of connected graphs with $k$ vertices and $k-1+l$ edges when $k,l$ approach infinity, reproving a result of Bender, Canfield and McKay. We use the {\em probabilistic method}, analyzing breadth-first search on…