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We define a simple model of conformal field theory in random space-time environments, which we refer to as stochastic conformal field theory. This model accounts for the effects of dilute random impurities in strongly interacting critical…

Subsequent to the ideas presented in our previous papers [J.Phys.: Condens. Matter {\bf 14} (2002) 13777 and Eur. Phys. J. B {\bf 42} (2004) 529], we discuss here in detail a new analytical approach to calculating the phase-diagram for the…

We study a class of stochastic processes of the type $\frac{d^n x}{dt^n}= v_0\, \sigma(t)$ where $n>0$ is a positive integer and $\sigma(t)=\pm 1$ represents an `active' telegraphic noise that flips from one state to the other with a…

Assume that one observes the $k$th, $2k$th$,\ldots,nk$th value of a Markov chain $X_{1,h},\ldots,X_{nk,h}$. That means we assume that a high frequency Markov chain runs in the background on a very fine time grid but that it is only observed…

Sampling from learned high-dimensional distributions is a foundational computational problem. We introduce U-turn chains: Markov chains obtained by iterating short forward-backward steps of a diffusion model, in which each step proposes a…

The paper presents a generalization of the local limit theorem on the convergence of inhomogeneous Markov chains to the diffusion limit for the case where the corresponding process coefficients satisfy weak regularity conditions and…

We consider the random walk on the hypercube which moves by picking an ordered pair $(i,j)$ of distinct coordinates uniformly at random and adding the bit at location $i$ to the bit at location $j$, modulo $2$. We show that this Markov…

Given a sequence $(\mathfrak{X}_i, \mathscr{K}_i)_{i=1}^\infty$ of Markov chains, the cut-off phenomenon describes a period of transition to stationarity which is asymptotically lower order than the mixing time. We study mixing times and…

Let $X$, $B$ and $Y$ be three Dirichlet, Bernoulli and beta independent random variables such that $X\sim \mathcal{D}(a_0,...,a_d),$ such that $\Pr(B=(0,...,0,1,0,...,0))=a_i/a$ with $a=\sum_{i=0}^da_i$ and such that $Y\sim \beta(1,a).$ We…

In this paper we show that the limiting distribution of the real and the imaginary part of the double Fourier transform of a stationary random field is almost surely an independent vector with Gaussian marginal distributions, whose variance…

We formulate a new model for transport in stochastic media with long-range spatial correlations where exponential attenuation (controlling the propagation part of the transport) becomes power law. Direct transmission over optical distance…

In the paper, we study a new rate of convergence estimate for homogeneous discrete-time nonlinear Markov chains based on the Markov-Dobrushin condition. This result generalizes the convergence estimates for any positive number of transition…

The cutoff phenomenon is an abrupt transition from out of equilibrium to equilibrium undergone by certain Markov processes in the limit where the size of the state space tends to infinity: instead of decaying gradually over time, their…

We study a colored generalization of the famous simple-switch Markov chain for sampling the set of graphs with a fixed degree sequence. Here we consider the space of graphs with colored vertices, in which we fix the degree sequence and…

Consider the map $(x, y) \mapsto (x + \epsilon^{-\alpha} \sin (2\pi x) + \epsilon^{-1-\alpha}z, z + \epsilon \sin(2\pi x))$, which is conjugate to the Chirikov standard map with a large parameter. The parameter value $\alpha = 1$ is related…

In this paper, we propose a new Markov chain which generalizes random-to-random shuffling on permutations to random-to-random shuffling on linear extensions of a finite poset of size $n$. We conjecture that the second largest eigenvalue of…

The cutoff phenomenon, conceptualized at the origin for finite Markov chains, states that for a parametric family of evolution equations, started from a point, the distance towards a long time equilibrium may become more and more abrupt for…

Consider a sequence $P_n$ of positive recurrent transition matrices or kernels that approximate a limiting infinite state matrix or kernel $P_{\infty}$. Such approximations arise naturally when one truncates an infinite state Markov chain…

The mean square displacement per collision of a molecule immersed in a gas at equilibrium is given by its mean square displacement between two consecutive collisions (mean square free path) corrected by a prefactor in the form of a series.…

Cylindrical lattice diffusion limited aggregation (DLA), with a narrow width N, is solved for site-sticking conditions using a Markovian matrix method (which was previously developed for the bond-sticking case). This matrix contains the…