相关论文: Path length distribution in two-dimensional causal…

We consider a directed graph on the 2-dimensional integer lattice, placing a directed edge from vertex $(i_1,i_2)$ to $(j_1,j_2)$, whenever $i_1 \le j_1$, $i_2 \le j_2$, with probability $p$, independently for each such pair of vertices.…

Previous studies of kinetic transport in the Lorentz gas have been limited to cases where the scatterers are distributed at random (e.g. at the points of a spatial Poisson process) or at the vertices of a Euclidean lattice. In the present…

Modularity is a key organizing principle in real-world large-scale complex networks. Many real-world networks exhibit modular structures such as transportation infrastructures, communication networks and social media. Having the knowledge…

We are given k points (events) in (n+1)-dimensional Minkowski space. Using the theory of hyperplane arrangments and chromatic polynomials, we obtain information the number of different orders in which the events can occur in different…

This article tackles the problem of existence and classification of maximal growth distributions on smooth manifolds. We show that maximal growth distributions of rank$>2$ abide by a full $h$-principle in all dimensions. We make use of M.…

A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures on Euclidean space. The theory is based…

We discuss the definition and measurability questions of random fractals and find under certain conditions a formula for upper and lower Minkowski dimensions. For the case of a random self-similar set we obtain the packing dimension.

In the present paper we introduce and study finite point subsets of a special kind, called optimum distributions, in the n-dimensional unit cube. Such distributions are closely related with known (delta,s,n)-nets of low discrepancy. It…

Networks in nature are often formed within a spatial domain in a dynamical manner, gaining links and nodes as they develop over time. We propose a class of spatially-based growing network models and investigate the relationship between the…

In this paper, we consider $N$ non-intersecting Bessel paths starting at $x=a\geq 0$, and conditioned to end at the origin $x=0$. We derive the explicit formula of the distribution function for the maximum height. Depending on the starting…

A method to compute the full hierarchy of the critical subsets of a density field is presented. It is based on a watershed technique and uses a probability propagation scheme to improve the quality of the segmentation by circumventing the…

Causal sets are locally finite, partially ordered sets (posets), which are considered as discrete models of spacetimes. On the one hand, causal sets corresponding to a spacetime manifold are commonly generated with a random process called…

The distribution function of particles over clusters is proposed for a system of identical intersecting spheres, the centres of which are uniformly distributed in space. Consideration is based on the concept of the rank number of clusters,…

We analyze the statistics of the shortest and fastest paths on the road network between randomly sampled end points. To a good approximation, these optimal paths are found to be directed in that their lengths (at large scales) are linearly…

Let L_n denote the lowest crossing of the 2n \times 2n square box B(n) centered at the origin for critical site percolation on Z^2 or critical site percolation on the triangular lattice imbedded in Z^2, and denote by Q_n the set of pivotal…

The aim in many sciences is to understand the mechanisms that underlie the observed distribution of variables, starting from a set of initial hypotheses. Causal discovery allows us to infer mechanisms as sets of cause and effect…

We study the structure of a uniformly randomly chosen partial order of width 2 on n elements. We show that under the appropriate scaling, the number of incomparable elements converges to the height of a one dimensional Brownian excursion at…

We study the distribution of optimal path lengths in random graphs with random weights associated with each link (``disorder''). With each link $i$ we associate a weight $\tau_i = \exp(ar_i)$ where $r_i$ is a random number taken from a…

A well-known open problem on the behavior of optimal paths in random graphs in the strong disorder regime, formulated by statistical physicists, and supported by a large amount of numerical evidence over the last decade [31,32,38,70] is as…

We consider partitions of a point set into two parts, and the lengths of the minimum spanning trees of the original set and of the two parts. If $w(P)$ denotes the length of a minimum spanning tree of $P$, we show that every set $P$ of $n…