Related papers: A probabilistic approach to the leader problem in …
For random $d$-regular graphs on $N$ vertices with $1 \ll d \ll N^{2/3}$, we develop a $d^{-1/2}$ expansion of the local eigenvalue distribution about the Kesten-McKay law up to order $d^{-3}$. This result is valid up to the edge of the…
We are interested in assigning a pre-specified number of nodes as leaders in order to minimize the mean-square deviation from consensus in stochastically forced networks. This problem arises in several applications including control of…
Graph-theoretic tools and techniques have seen wide use in the multi-agent systems literature, and the unpredictable nature of some multi-agent communications has been successfully modeled using random communication graphs. Across both…
A scaling limit for the simple random walk on the largest connected component of the Erdos-Renyi random graph in the critical window is deduced. The limiting diffusion is constructed using resistance form techniques, and is shown to satisfy…
Let $\mathcal{G}(N,\frac 1Nt_N)$ be the Erd\H{o}s-R\'enyi graph with connection probability $\frac 1Nt_N\sim t/N$ as $N\to\infty$ for a fixed $t\in(0,\infty)$. We derive a large-deviations principle for the empirical measure of the sizes of…
Assume for a graph $G=(V,E)$ and an initial configuration, where each node is blue or red, in each discrete-time round all nodes simultaneously update their color to the most frequent color in their neighborhood and a node keeps its color…
Computing the rate of evolution in spatially structured populations is difficult. A key quantity is the fixation time of a single mutant with relative reproduction rate $r$ which invades a population of residents. We say that the fixation…
We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known…
We investigate the component sizes of the critical configuration model, as well as the related problem of critical percolation on a supercritical configuration model. We show that, at criticality, the finite third moment assumption on the…
In the deterministic binary majority process we are given a simple graph where each node has one out of two initial opinions. In every round, every node adopts the majority opinion among its neighbors. By using a potential argument first…
We study a discrete model of coagulation, involving a large number $N$ of particles. Pairs of particles are given i.i.d exponential clocks with parameter $1/N$. When a clock rings, a link between the corresponding pair of particles is…
We study the problem of detecting the edge correlation between two random graphs with $n$ unlabeled nodes. This is formalized as a hypothesis testing problem, where under the null hypothesis, the two graphs are independently generated;…
We study the robust communication complexity of maximum matching. Edges of an arbitrary $n$-vertex graph $G$ are randomly partitioned between Alice and Bob independently and uniformly. Alice has to send a single message to Bob such that Bob…
The cover time of a graph is a celebrated example of a parameter that is easy to approximate using a randomized algorithm, but for which no constant factor deterministic polynomial time approximation is known. A breakthrough due to Kahn,…
The aim of this paper is to develop a method for proving almost sure convergence in Gromov-Hausodorff-Prokhorov topology for a class of models of growing random graphs that generalises R\'emy's algorithm for binary trees. We describe the…
We investigate the dynamic formation of regular random graphs. In our model, we pick a pair of nodes at random and connect them with a link if both of their degrees are smaller than d. Starting with a set of isolated nodes, we repeat this…
We present a uniform self-stabilizing algorithm, which solves the problem of distributively finding a minimum diameter spanning tree of an arbitrary positively real-weighted graph. Our algorithm consists in two stages of stabilizing…
The maximum likelihood threshold (MLT) of a graph $G$ is the minimum number of samples to almost surely guarantee existence of the maximum likelihood estimate in the corresponding Gaussian graphical model. We give a new characterization of…
Bassino et al. (arXiv:1907.08517) have shown that uniform random co-graphs (graphs without induced $P_4$) of size $n$ converge to a certain non-deterministic graphon. The edge-density of this graphon is a random variable $\Lambda \in [0,1]$…
We study the largest component of a random (multi)graph on n vertices with a given degree sequence. We let n tend to infinity. Then, under some regularity conditions on the degree sequences, we give conditions on the asymptotic shape of the…