Related papers: Convergence and coupling for spin glasses and hard…
There has been a recent surge of powerful tools to show rapid mixing of Markov chains, via functional inequalities such as Poincar\'e inequalities. In many situations, Markov chains fail to mix rapidly from a worst-case initialization, yet…
Couplings play a central role in contemporary Markov chain Monte Carlo methods and in the analysis of their convergence to stationarity. In most cases, a coupling must induce relatively fast meeting between chains to ensure good…
We analyze the convergence of the irreversible event-chain Monte Carlo algorithm for continuous spin models in the presence of topological excitations. In the two-dimensional XY model, we show that the local nature of the Markov-chain…
Upper bounds are derived on the total variation distance between the invariant distributions of two stochastic matrices differing on a subset W of rows. Such bounds depend on three parameters: the mixing time and the minimal expected…
We show how to apply the absorbing Markov chain Monte Carlo algorithm of Novotny to simulate kinetically constrained models of glasses. We consider in detail one-spin facilitated models, such as the East model and its generalizations to…
The essential role of synthetic spin-orbit coupling in discovering new topological matter phases with cold atoms is widely acknowledged. However, the engineering of spin-orbit coupling remains unclear for arbitrary-spin models due to the…
We define a discrete-time Markov chain for abstract polymer models and show that under sufficient decay of the polymer weights, this chain mixes rapidly. We apply this Markov chain to polymer models derived from the hard-core and…
We propose an efficient Markov Chain Monte Carlo method for sampling equilibrium distributions for stochastic lattice models, capable of handling correctly long and short-range particle interactions. The proposed method is a Metropolis-type…
Infinite-range spin-glass models with Levy-distributed interactions show a spin-glass transition with similarities to both the Sherrington-Kirkpatrick model and to disordered spin systems on finite connectivity random graphs. Despite the…
Hierarchical spin-glasses are Ising spin models defined by recursively coupling together two equally-sized sub-systems. In this work a new hierarchical spin system is introduced wherein the sub-systems are recursively coupled together…
We present a coupling framework to upper bound the total variation mixing time of various Metropolis-adjusted, gradient-based Markov kernels in the `high acceptance regime'. The approach uses a localization argument to boost local mixing of…
We present mode-coupling theory (MCT) results for densely packed hard-sphere fluids confined between two parallel walls and compare them quantitatively to computer simulations. The numerical solution of MCT is calculated for the first time…
The problem of sampling from the stationary distribution of a Markov chain finds widespread applications in a variety of fields. The time required for a Markov chain to converge to its stationary distribution is known as the classical…
We present a nonlocal Monte Carlo algorithm with particle swaps that greatly accelerates thermalization of soft sphere binary mixtures in the glassy region. Our first results show that thermalization of systems of hundreds of particles is…
Parallel tempering (PT) methods are a popular class of Markov chain Monte Carlo schemes used to sample complex high-dimensional probability distributions. They rely on a collection of $N$ interacting auxiliary chains targeting tempered…
We use coupling to study the time taken until the distribution of a statistic on a Markov chain is close to its stationary distribution. Coupling is a common technique used to obtain upper bounds on mixing times of Markov chains, and we…
We review several parallel tempering schemes and examine their main ingredients for accuracy and efficiency. The present study covers two selection methods of temperatures and several choices for the exchange of replicas, including a recent…
The complex behavior of confined fluids arising due to a competition between layering and local packing can be disentangled by considering quasi-confined liquids, where periodic boundary conditions along the confining direction restore…
We present an algorithm for finding ground states of two dimensional spin glass systems based on ideas from matrix product states in quantum information theory. The algorithm works directly at zero temperature and defines an approximate…
There has been a recent surge of interest in coupling methods for Markov chain Monte Carlo algorithms: they facilitate convergence quantification and unbiased estimation, while exploiting embarrassingly parallel computing capabilities.…