Related papers: Spectrum of large random reversible Markov chains:…
We investigate the spectra of adjacency matrices of multiplex networks under random matrix theory (RMT) framework. Through extensive numerical experiments, we demonstrate that upon multiplexing two random networks, the spectra of the…
Classical linear regression is considered for a case when regression parameters depend on the external random environment. The last is described as a continuous time Markov chain with finite state space. Here the expected sojourn times in…
It recently has been found that methods of the statistical theories of spectra can be a useful tool in the analysis of spectra far from levels of Hamiltonian systems. Several examples originate from areas, such as quantitative linguistics…
In this paper, we consider a general class of two-time-scale Markov chains whose transition rate matrix depends on a parameter $\lambda>0$. We assume that some transition rates of the Markov chain will tend to infinity as…
Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all…
We consider reversible random walks in random environment obtained from symmetric long--range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and…
We compute spectra of large stochastic matrices $W$, defined on sparse random graphs, where edges $(i,j)$ of the graph are given positive random weights $W_{ij}>0$ in such a fashion that column sums are normalized to one. We compute spectra…
This paper concerns the long-term behaviour of a system of interacting random walks labeled by vertices of a finite graph. The model is reversible which allows to use the method of electric networks in the study. In addition, examples of…
We develop Markov chain mixing time estimates for a class of Markov chains with restricted transitions. We assume transitions may occur along a cycle of $n$ nodes and on $n^\gamma$ additional edges, where $\gamma < 1$. We find that the…
With a sequence of regressions, one may generate joint probability distributions. One starts with a joint, marginal distribution of context variables having possibly a concentration graph structure and continues with an ordered sequence of…
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…
A Markov chain is considered whose states are orderings of an underlying fixed tree and whose transitions are local "random-to-front" reorderings, driven by a probability distribution on subsets of the leaves. The eigenvalues of the…
We numerically investigate the low-lying entanglement spectrum of the ground state of random one-dimensional spin chains obtained after partition of the chain into two equal halves. We consider two paradigmatic models: the spin-1/2 random…
By randomly removing a fraction of levels from a given spectrum a model is constructed that describes a crossover from this spectrum to a Poisson spectrum. The formalism is applied to the transitions towards Poisson from random matrix…
In this note we consider a Markov chain formed by a finite system of interacting birth-and-death processes on a finite state space. We study an asymptotic behaviour of the Markov chain as its state space becomes large. In particular, we…
We analyze the absolute spectral gap of Markov chains on graphs obtained from a cycle of $n$ vertices and perturbed only at approximately $n^{1/\rho}$ random locations with an appropriate, possibly sparse, interconnection structure.…
We analyze spectral properties of a quantum graph in the form of a ring chain with a $\delta$ coupling in the vertices exposed to a homogeneous magnetic field perpendicular to the graph plane. We find the band spectrum in the case when the…
Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with the…
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…
For a Markov chain both the detailed balance condition and the cycle Kolmogorov condition are algebraic binomials. This remark suggests to study reversible Markov chains with the tool of Algebraic Statistics, such as toric statistical…