Related papers: The Critical Mean-field Chayes-Machta Dynamics
Large continuous-time Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry and biology. We propose a constructive graph-algorithmic approach to determine the sequence of critical…
We start from the Theory of Random Point Processes to derive n-point coupled master equations describing the continuous dynamics of discrete variables in random graphs. These equations constitute a hierarchical set of approximations that…
We consider the random walk Metropolis algorithm on $\mathbb{R}^n$ with Gaussian proposals, and when the target probability measure is the $n$-fold product of a one-dimensional law. In the limit $n\to\infty$, it is well known (see [Ann.…
Consider a sequence of continuous-time irreducible reversible Markov chains and a sequence of initial distributions, $\mu_n$. The sequence is said to exhibit $\mu_n$-cutoff if the convergence to stationarity in total variation distance is…
We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…
Applying the mathematical circulation theory of Markov chains, we investigate the synchronized stochastic dynamics of a discrete network model of yeast cell-cycle regulation where stochasticity has been kept rather than being averaged out.…
How a system initially at infinite temperature responds when suddenly placed at finite temperatures is a way to check the existence of phase transitions. It has been shown in [R. da Silva, IJMPC 2023] that phase transitions are imprinted in…
A cellular automaton model is presented for random walkers with biologically motivated interactions favoring local alignment and leading to collective motion or swarming behavior. The degree of alignment is controlled by a sensitivity…
We prove an inequality on decision trees on monotonic measures which generalizes the OSSS inequality on product spaces. As an application, we use this inequality to prove a number of new results on lattice spin models and their…
Recently, several complex network approaches to time series analysis have been developed and applied to study a wide range of model systems as well as real-world data, e.g., geophysical or financial time series. Among these techniques,…
Establishing central limit theorems (CLTs) for ergodic averages of Markov chains is a fundamental problem in probability and its applications. Since the seminal work~\cite{MR834478}, a vast literature has emerged on the sufficient…
The random-cluster model is a dependent percolation model that has applications in the study of Ising and Potts models. In this paper, several new results are obtained for the random-cluster model on nonamenable graphs with cluster…
Consider Glauber dynamics for the Ising model on a graph of $n$ vertices. Hayes and Sinclair showed that the mixing time for this dynamics is at least $n\log n/f(\Delta)$, where $\Delta$ is the maximum degree and $f(\Delta) = \Theta(\Delta…
Autonomous randomly coupled neural networks display a transition to chaos at a critical coupling strength. We here investigate the effect of a time-varying input on the onset of chaos and the resulting consequences for information…
We consider the problem of clustering grouped data with possibly non-exchangeable groups whose dependencies can be characterized by a known directed acyclic graph. To allow the sharing of clusters among the non-exchangeable groups, we…
We study the worst-case mixing time of the global Kawasaki dynamics for the fixed-magnetization Ising model on the class of graphs of maximum degree $\Delta$. Proving a conjecture of Carlson, Davies, Kolla, and Perkins, we show that below…
Given an underlying graph, we consider the following \emph{dynamics}: Initially, each node locally chooses a value in $\{-1,1\}$, uniformly at random and independently of other nodes. Then, in each consecutive round, every node updates its…
The random--anisotropy Blume--Emery--Griffiths model, which has been proposed to describe the critical behavior of $^3$He--$^4$He mixtures in a porous medium, is studied in the pair approximation of the cluster variation method extended to…
The Ising model is widely regarded as the most studied model of spin-systems in statistical physics. The focus of this paper is its dynamic (stochastic) version, the Glauber dynamics, introduced in 1963 and by now the most popular means of…
Random walks on expanders play a crucial role in Markov Chain Monte Carlo algorithms, derandomization, graph theory, and distributed computing. A desirable property is that they are rapidly mixing, which is equivalent to having a spectral…