The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between particles. We rigorously prove that for the stationary probability measure there is a background phase at some critical density and for large system size esse...

In a spatial data analysis problem, usually we build a hierarchical model with spatial structure described though random effects using a Gaussian process. If the sample size is very large, exact likelihood based inference becomes unstable and, eventually, infeasible since it involves computing quadratic forms and determinants associate with a large covariance matrix. If we wish to fit a Bayesia...

It is known that the stationary distribution of the random walk process is dependent on the structure of the network. This could provide us a solution of the network reconstruction. However, the stationary distribution of the random walk process can only reflect the relative size of node degrees directly, how to infer the real connection is still a problem. In this paper, we will propose a meth...

Many stochastic models have been investigated for quantum mechanics because of its stochastic nature. For example, Cohendet et al. introduced a dichotomic variable to quantum phase space and proposed a background Markov process for the time evolution of the Wigner function. However, in their method we need the whole distribution function to determine the next step of a particle under considerat...

By far, the analysis of particles heat and mass transfer in open nanosystems is of noticeable importance both in theoretical and practical researches. Due to a slotted and cylindrical systems resort we have been able to carry out some essential experimental investigations as well as provide new theoretical computations. The distinctive feature of nanosystems gas particles transport research is ...

In this talk we present a procedure to test if a stationary process is Gaussian. The observation consists in a finite sample of a path of the process. The test is based on the fact (stablished in Cuesta-Albertos et al. (2007)) that, almost surely, a distribution is Gaussian iff a randomly chosen onedimensional projection is Gaussian, thus transforming the problema of testing the infinite-dimens...

For general, almost surely absorbed Markov processes, we obtain necessary and sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process (the process conditioned to never be absorbed). We apply these results to one-dimensional birth and death proce...

In this paper, we show large deviations for random step functions of type

Extensive evidence suggests that items are not encoded independently in visual short-term memory (VSTM). However, previous research has not quantitatively considered how the encoding of an item influences the encoding of other items. Here, we model the dependencies among VSTM representations using a multivariate Gaussian distribution with a stimulus-dependent mean and covariance matrix. We repo...

We find logarithmic asymptotics of L2-small deviation probabilities for weighted stationary Gaussian processes (both for real and complex-valued) having power-type discrete or continuous spectrum. As in [12], our results are based on the spectral theory of pseudodifferential operators developed by Birman and Solomyak.