The lattice gas model in equilibrium is considered. We give a lower bound of the density-density time correlation for large time, which involves the bulk diffusion matrix in a physically natural way.

The law of a random tree constructed within a Brownian excursion is calculated conditional on knowing the occupation measure of the excursion. In previous work David Aldous has used random walk approximations to obtain this result. Here it is deduced…

We construct a Brownian path conditioned on its minimum value over a fixed time interval by a simple transformation of a Brownian bridge.

Noise sensitivity of functions on the leaves of a binary tree is studied, and a hypercontractive inequality is obtained. We deduce that the spider walk is not noise stable.

Recently, Kalvin M. Jansons derived in an elegant way the Laplace transform of the time spent by an excursion above a given level $a>0$. This result can also be derived from previous work of the author on the occupation time…

We study a class of Borel probability measures, called correlation measures. Our results are of two types: first, we give explicit constructions of non-trivial correlation measures; second, we examine some of the properties of the set of correlation measures. In…

In this note, we study the Gaussian fluctuations of the edge occupation measure for a reversible Markov chain and give a nice description of the covariance matrix. Then we give some large deviations results concerning this occupation measure.

We present a Gaussian correlation inequality which is closely related to a result of Schechtman, Schlumprecht and Zinn (1998) on the well-known Gaussian correlation conjecture. The usefulness of the inequality is demonstrated by several important applications to the estimates of…

Consider two exchangeable sequences $(X_k)_{k \in N}$ and $(\hat{X}_k)_{k \in N}$ with the property that $S_n \equiv \sum_{k=1}^n X_k$ and $\hat{S}_n \equiv \sum_{k=1}^n \hat{X}_k$ have the same distribution for all $n \in N$. David Aldous posed the following question. Does…

Rogers-Pitman have shown that the sum of the absolute value of $B^{(\mu)}$, Brownian motion with constant drift $\mu$, and its local time $L^{(\mu)}$ is a diffusion $R^{(\mu)}$. We exploit the intertwining relation between $B^{(\mu)}$ and $R^{(\mu)}$ to show that the…