Related papers: On the mixing time in the Wang-Landau algorithm
We present an efficient sampling method for computing a partition function and accelerating configuration sampling. The method performs a random walk in the $\lambda$ space, with $\lambda$ being any thermodynamic variable that characterizes…
The distribution of the "mixing time" or the "time to stationarity" in a discrete time irreducible Markov chain, starting in state i, can be defined as the number of trials to reach a state sampled from the stationary distribution of the…
Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the…
We study the mixing time of the Rook's Walk Markov chain on a $d$-dimensional chess board of side length $n\geq 3$, where a rook moves by first selecting an axis uniformly at random and then selecting a new position along that axis…
In this paper, we consider the Markov-Chain Monte Carlo (MCMC) approach for random sampling of combinatorial objects. The running time of such an algorithm depends on the total mixing time of the underlying Markov chain and is unknown in…
Given an irreducible discrete-time Markov chain on a finite state space, we consider the largest expected hitting time $T(\alpha)$ of a set of stationary measure at least $\alpha$ for $\alpha\in(0,1)$. We obtain tight inequalities among the…
We prove tight mixing time bounds for natural random walks on bases of matroids, determinantal distributions, and more generally distributions associated with log-concave polynomials. For a matroid of rank $k$ on a ground set of $n$…
Monte Carlo simulations using Wang-Landau sampling are performed to study three-dimensional chains of homopolymers on a lattice. We confirm the accuracy of the method by calculating the thermodynamic properties of this system. Our results…
We describe an exact approach for calculating transition probabilities and waiting times in finite-state discrete-time Markov processes. All the states and the rules for transitions between them must be known in advance. We can then…
The statistics of first-passage times of random walks to target sites has proved to play a key role in determining the kinetics of space exploration in various contexts. In parallel, the number of distinct sites visited by a random walker…
We introduce a non-equilibrium discrete-time random walk model on multiplex networks, in which at each time step the walker first undergoes a random jump between neighboring nodes in the same layer, and then tries to hop from one node to…
We address the problem of inferring the topology of a wireless network using limited observational data. Specifically, we assume that we can detect when a node is transmitting, but no further information regarding the transmission is…
We study the lattice random walk dynamics in a heterogeneous space of two media separated by an interface and having different diffusivity and bias. Depending on the position of the interface, there exist two exclusive ways to model the…
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 finite-time mixing in time-periodic open flow systems. We describe the transport of densities in terms of a transfer operator, which is represented by the transition matrix of a finite-state Markov chain. The transport processes in…
We investigate the mixing properties of a model of reversible Markov chains in random environment, which notably contains the simple random walk on the superposition of a deterministic graph and a second graph whose vertex set has been…
This paper discusses some convergence properties in the entropic sampling Monte Carlo methods with multiple random walkers, particularly in the Wang-Landau (WL) and $1/t$ algorithms. The classical algorithms are modified by the use of $m$…
Under certain conditions, the dynamics of coarse-grained models of solvated proteins can be described using a Markov state model, which tracks the evolution of populations of configurations. The transition rates among states that appear in…
Metropolis algorithm has been extensively employed for simulating a canonical ensemble and estimating macroscopic properties of a closed system at any desired temperature. A mechanical property, like energy can be calculated by averaging…
We obtain an exact formula for the first-passage time probability distribution for random walks on complex networks using inverse Laplace transform. We write the formula as the summation of finitely many terms with different frequencies…