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In the noisy channel model from coding theory, we wish to detect errors introduced during transmission by optimizing various parameters of the code. Bennett, Dudek, and LaForge framed a variation of this problem in the language of…
The possibility of achieving a gauge coupling grand unification by increasing the QCD degrees of freedom at higher energies is investigated. When confronted with precision low-energy data, the generic weak-mixing angle relation…
We present a new lower bound on the spectral gap of the Glauber dynamics for the Gibbs distribution of a spectrally independent $q$-spin system on a graph $G = (V,E)$ with maximum degree $\Delta$. Notably, for several interesting examples,…
Motivated by the community detection problem in Bayesian inference, as well as the recent explosion of interest in spin glasses from statistical physics, we study the classical Glauber dynamics for sampling from Ising models with sparse…
Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph $G$, a temporal graph is represented by assigning a set of integer time-labels to every edge $e$ of $G$, indicating the…
Let $\gS=(V,E)$ be a finite, $d$-regular bipartite graph. For any $\lambda>0$ let $\pi_\lambda$ be the probability measure on the independent sets of $\gS$ in which the set $I$ is chosen with probability proportional to $\lambda^{|I|}$…
We prove that Broder's Markov chain for approximate sampling near-perfect and perfect matchings is not rapidly mixing for Hamiltonian, regular, threshold and planar bipartite graphs, filling a gap in the literature. In the second part we…
This paper introduces a concept of approximate spectral gap to analyze the mixing time of Markov Chain Monte Carlo (MCMC) algorithms for which the usual spectral gap is degenerate or almost degenerate. We use the idea to analyze a class of…
We study the mixing time of systematic scan Markov chains on finite spin systems. It is known that, in a single site setting, the mixing time of systematic scan can be bounded in terms of the influences sites have on each other. We…
We consider the Ising, and more generally, $q$-state Potts Glauber dynamics on random $d$-regular graphs on $n$ vertices at low temperatures $\beta \gtrsim \frac{\log d}{d}$. The mixing time is exponential in $n$ due to a bottleneck between…
We consider a random graph in which vertices can have one of two possible colours. Each vertex switches its colour at a rate that is proportional to the number of vertices of the other colour to which it is connected by an edge. Each edge…
The problem of uniformly sampling hypergraph independent sets is revisited. We design an efficient perfect sampler for the problem under a condition similar to that of the asymmetric Lov\'asz Local Lemma. When applied to $d$-regular…
We examine various perspectives on the decay of correlation for the uniform distribution over proper $q$-edge colorings of graphs with maximum degree $\Delta$. First, we establish the coupling independence property when $q\ge 3\Delta$ for…
Ge and Stefankovic have recently introduced a novel two-variable graph polynomial. When specialised to a bipartite graphs G and evaluated at the point (1/2,1) this polynomial gives the number of independent sets in the graph. Inspired by…
We investigate the phase diagram of disordered copolymers at the interface between two selective solvents, and in particular its weak-coupling behavior, encoded in the slope $m_c$ of the critical line at the origin. In mathematical terms,…
An edge-coloring of a graph G is acyclic if it is a proper edge-coloring of G and every cycle contains at least three colors. We prove that every graph with maximum degree Delta has an acyclic edge-coloring with at most 4 Delta - 4 colors,…
We prove two results on the mixing times of Markov chains for two-spin systems. First, we show that the Glauber dynamics mixes in polynomial time for the Gibbs distributions of antiferromagnetic two-spin systems at the critical threshold of…
The switch chain is a well-known Markov chain for sampling directed graphs with a given degree sequence. While not ergodic in general, we show that it is ergodic for regular degree sequences. We then prove that the switch chain is rapidly…
We investigate the upper chromatic number of the hypergraph formed by the points and the $k$-dimensional subspaces of $\mathrm{PG}(n,q)$; that is, the most number of colors that can be used to color the points so that every $k$-subspace…
For general antiferromagnetic 2-spin systems, including the hardcore model and the antiferromagnetic Ising model, there is an $\mathsf{FPTAS}$ for the partition function on graphs of maximum degree $\Delta$ when the infinite regular tree…