Related papers: Low-temperature Sampling on Sparse Random Graphs
Approximating the partition function of the ferromagnetic Ising model with general external fields is known to be #BIS-hard in the worst case, even for bounded-degree graphs, and it is widely believed that no polynomial-time approximation…
Finding independent sets of maximum size in fixed graphs is well known to be an NP-hard task. Using scaling limits, we characterise the asymptotics of sequential degree-greedy explorations and provide sufficient conditions for this…
The zero-temperature Glauber dynamics is used to investigate the persistence probability $P(t)$ in the Potts model with $Q=3,4,5,7,9,12,24,64, 128$, $256, 512, 1024,4096,16384 $,..., $2^{30}$ states on {\it directed} and {\it undirected}…
We revisit the probabilistic construction of sparse random matrices where each column has a fixed number of nonzeros whose row indices are drawn uniformly at random with replacement. These matrices have a one-to-one correspondence with the…
The study of complex systems is limited by the fact that only few variables are accessible for modeling and sampling, which are not necessarily the most relevant ones to explain the systems behavior. In addition, empirical data typically…
Correlation analysis is a fundamental problem in statistics. In this paper, we consider the correlation detection problem between a pair of Erdos-Renyi graphs. Specifically, the problem is formulated as a hypothesis testing problem: under…
Baker devised a powerful technique to obtain approximation schemes for various problems restricted to planar graphs. Her technique can be directly extended to various other graph classes, among the most general ones the graphs avoiding a…
We consider the problem of inferring a graphical Potts model on a population of variables, with a non-uniform number of Potts colors (symbols) across variables. This inverse Potts problem generally involves the inference of a large number…
We study the algorithmic tractability of finding large independent sets in dense random hypergraphs. In the sparse regime, much of the natural algorithms can be formulated within either the local or the low-degree polynomial (LDP)…
We study the partition functions associated with non-intersecting polymers in a random environment. By considering paths in series and in parallel, the partition functions carry natural notions of subadditivity, allowing the effective study…
Sampling of signals defined over the nodes of a graph is one of the crucial problems in graph signal processing. While in classical signal processing sampling is a well defined operation, when we consider a graph signal many new challenges…
Over the last years, there has been a significant amount of work studying the power of specific classes of computationally efficient estimators for multiple statistical parametric estimation tasks, including the estimators classes of…
In this work, we investigate the sampling and reconstruction of spectrally $s$-sparse bandlimited graph signals governed by heat diffusion processes. We propose a random space-time sampling regime, referred to as {randomized} dynamical…
Graphical data arises naturally in several modern applications, including but not limited to internet graphs, social networks, genomics and proteomics. The typically large size of graphical data argues for the importance of designing…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
We prove algorithmic weak and \Szemeredi{} regularity lemmas for several classes of sparse graphs in the literature, for which only weak regularity lemmas were previously known. These include core-dense graphs, low threshold rank graphs,…
As large graph datasets become increasingly common across many fields, sampling is often needed to reduce the graphs into manageable sizes. This procedure raises critical questions about representativeness as no sample can capture the…
Motivated by an application in community detection, we consider an \ER random graph conditioned on the rare event that all connected components are fully connected. Such graphs can be considered as partitions of vertices into cliques.…
Network (or graph) sparsification compresses a graph by removing inessential edges. By reducing the data volume, it accelerates or even facilitates many downstream analyses. Still, the accuracy of many sparsification methods, with…
We study continuous time Glauber dynamics for random configurations with local constraints (e.g. proper coloring, Ising and Potts models) on finite graphs with $n$ vertices and of bounded degree. We show that the relaxation time (defined as…