Related papers: Information Transmission under Random Emission Con…
A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…
In random access protocols, the service rate depends on the number of stations with a packet buffered for transmission. We demonstrate via numerical analysis that this state-dependent rate along with the consideration of Poisson traffic and…
The Central Limit Theorem provides a foundation for inferential statistics and hypothesis testing. It describes how standardized statistics behave under repeated sampling from large populations. However, if the size of the sample (n)…
The paper is devoted to the spreading of a message within the random graph evolving by the Norros-Reittu preferential attachment model. The latter model forms random Poissonian numbers of edges between newly added nodes and existing ones.…
Shannon's Capacity Theorem is the main concept behind the Theory of Communication. It says that if the amount of information contained in a signal is smaller than the channel capacity of a physical media of communication, it can be…
In this article, we study the large-population limit of interacting particle systems posed on weighted random graphs. In that aim, we introduce a general framework for the construction of weighted random graphs, generalizing the concept of…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
We consider a line of terminals which is connected by packet erasure channels and where random linear network coding is carried out at each node prior to transmission. In particular, we address an online approach in which each terminal has…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
This paper initiates the study of the impact of failures on the fundamental problem of \emph{information spreading} in the Vertex-Congest model, in which in every round, each of the $n$ nodes sends the same $O(\log{n})$-bit message to all…
We consider the problem of communicating a sequence of concepts, i.e., unknown and potentially stochastic maps, which can be observed only through examples, i.e., the mapping rules are unknown. The transmitter applies a learning algorithm…
We consider a conditionally Poissonian random graph model where the mean degrees, `capacities', follow a power-tailed distribution with finite mean and infinite variance. Such a graph of size $N$ has a giant component which is super-small…
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…
A growing random graph is constructed by successively sampling without replacement an element from the pool of virtual vertices and edges. At start of the process the pool contains $N$ virtual vertices and no edges. Each time a vertex is…
In this paper, the problem of distributed opportunistic channel access in wireless relaying is investigated. A relay network with multiple source-destination pairs and multiple relays is considered. All the source nodes contend through a…
In the random geometric graph $G(n,r_n)$, $n$ vertices are placed randomly in Euclidean $d$-space and edges are added between any pair of vertices distant at most $r_n$ from each other. We establish strong laws of large numbers (LLNs) for a…
This paper presents a stochastic geometry model for the investigation of fundamental information theoretic limitations in wireless networks. We derive a new unified multi-parameter cut-set bound on the capacity of networks of arbitrary…
We consider the problem of communication over a network containing a hidden and malicious adversary that can control a subset of network resources, and aims to disrupt communications. We focus on omniscient node-based adversaries, i.e., the…
We consider weakly interacting diffusions on time varying random graphs. The system consists of a large number of nodes in which the state of each node is governed by a diffusion process that is influenced by the neighboring nodes. The…
Constructing a minimal vertex cover of a graph can be seen as a prototype for a combinatorial optimization problem under hard constraints. In this paper, we develop and analyze message passing techniques, namely warning and survey…