相关论文: Yaglom limits can depend on the starting state

This paper surveys various results about Markov chains on general (non-countable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which…

For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. For the subcritical regime a kind of phase transition…

This paper develops a new class of conditional Markov jump processes with regime switching and paths dependence. The key novel feature of the developed process lies on its ability to switch the transition rate as it moves from one state to…

In quantum information processing, {using a receiver device to differentiate between two nonorthogonal states leads to a quantum error probability. The minimum possible error is} known as the Helstrom bound. In this work we study and…

We continue the study of the level-set percolation of the discrete Gaussian free field (GFF) on regular trees in the critical regime, initiated in arXiv:2302.02753. First, we derive a sharp asymptotic estimate for the probability that the…

The problem of pattern selection in absolutely unstable open flow systems is investigated by considering the example of Rayleigh-B\'{e}nard convection. The spatiotemporal structure of convection rolls propagating downstream in an externally…

In this paper, we investigate the functional central limit theorem for stochastic processes associated to partial sums of additive functionals of reversible Markov chains with general spate space, under the normalization standard deviation…

Testing for regime switching when the regime switching probabilities are specified either as constants (`mixture models') or are governed by a finite-state Markov chain (`Markov switching models') are long-standing problems that have also…

We establish metastability in the sense of Lebowitz and Penrose under practical and simple hypothesis for (families of) Markov chains on finite configuration space in some asymptotic regime, including the case of configuration space size…

Consider a system of interacting particles indexed by the nodes of a graph whose vertices are equipped with marks representing parameters of the model such as the environment or initial data. Each particle takes values in a countable state…

This paper analyzes stochastic networks consisting of finite capacity nodes with different classes of requests which move according to some routing policy. The Markov processes describing these networks do not, in general, have…

This study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in $\mathbb{Z}^2$ or in $\mathbb{Z}^3$. These models are immersed in multi-type particle systems with exclusion.…

The evolution of an isolated quantum system inevitably exhibits recurrence: the state returns to the vicinity of its initial condition after finite time. Despite its fundamental nature, a rigorous quantitative understanding of recurrence…

We study the ergodic behaviour of a discrete-time process $X$ which is a Markov chain in a stationary random environment. The laws of $X_t$ are shown to converge to a limiting law in (weighted) total variation distance as $t\to\infty$.…

We present a general method to derive the metastable behavior of weakly mixing Markov chains. This approach is based on properties of the resolvent equations and can be applied to metastable dynamics which do not satisfy the mixing…

We consider a Wigner-type ensemble, i.e. large hermitian $N\times N$ random matrices $H=H^*$ with centered independent entries and with a general matrix of variances $S_{xy}=\mathbb E|H_{xy}|^2$. The norm of $H$ is asymptotically given by…

We consider non-reversible random walks evolving on a potential field in a bounded domain of $\mathbb{R}^d$. We describe the complete metastable behavior of the random walk among the landscape of valleys, and we derive the Eyring-Kramers…

Random walks are a fundamental model in applied mathematics and are a common example of a Markov chain. The limiting stationary distribution of the Markov chain represents the fraction of the time spent in each state during the stochastic…

We develop a martingale approximation approach to studying the limiting behavior of quadratic forms of Markov chains. We use the technique to examine the asymptotic behavior of lag-window estimators in time series and we apply the results…

We study the critical branching random walk on $\mathbb{Z}^d$ started from a distant point $x$ and conditioned to hit some compact set $K$ in $\mathbb{Z}^d$. We are interested in the occupation time in $K$ and present its asymptotic…