相关论文: On meteors, earthworms and WIMPs

We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…

This paper investigates the consensus problem in almost sure sense for uncertain multi-agent systems with noises and fixed topology. By combining the tools of stochastic analysis, algebraic graph theory, and matrix theory, we analyze the…

A random graph evolution based on the interactions of N vertices is studied. During the evolution both the preferential attachment method and the uniform choice of vertices are allowed. The weight of a vertex means the number of its…

In this letter we study the NP-complete vertex cover problem on finite connectivity random graphs. When the allowed size of the cover set is decreased, a discontinuous transition in solvability and typical-case complexity occurs. This…

We consider random rooted maps without regard to their genus, with fixed large number of edges, and address the problem of limiting distributions for six different parameters: vertices, leaves, loops, root edges, root isthmus, and root…

We consider limits of equilibrium distributions as temperature approaches zero, for systems of infinitely many particles, and characterize the support of the limiting distributions. Such results are known for particles with positions on a…

We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we…

We examine some aspects of the recent results by K. Binder. The equilibrium formation/dissolution of droplets in finite systems is discussed in the context of the canonical and the grand canonical distributions.

This work deals with the average scattering entropy of quantum graphs. We explore this concept in several distinct scenarios that involve periodic, aperiodic and random distribution of vertices of distinct degrees. In particular, we compare…

We introduce a set of iterative equations that exactly solves the size distribution of components on small arbitrary graphs after the random removal of edges. We also demonstrate how these equations can be used to predict the distribution…

We consider the reversible adsorption of dimers on a regular lattice, where adsorption occurs on a finite fraction of sites selected randomly. By comparing this system to the pure system where all sites are available for adsorption, we show…

We study extremal problems about sets of integers that do not contain sumsets with summands of prescribed size. We analyse both finite sets and infinite sequences. We also study the connections of these problems with extremal problems of…

This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they…

This article is concerned with the long time behavior of neutral genetic population models, with fixed population size. We design an explicit, finite, exact, genealogical tree based representation of stationary populations that holds both…

The occurrence and the distribution of patterns of trees associated to natural numbers are investigated. Bounds from above and below are proven for certain natural quantities.

We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…

In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…

We consider statistics on permutations chosen uniformly at random from fixed parabolic double cosets of the symmetric group. We show that the distribution of fixed points is asymptotically Poisson and establish central limit theorems for…

Sampling algorithms, hypergraph degree sequences, and polytopes play a crucial role in statistical analysis of network data. This article offers a brief overview of open problems in this area of discrete mathematics from the point of view…

Distributed optimization for resource allocation problems is investigated and a sub-optimal continuous-time algorithm is proposed. Our algorithm has lower order dynamics than others to reduce burdens of computation and communication, and is…