An explicit coupling construction of random-cluster measures is presented. As one of the applications of the construction, the Potts model on amenable Cayley graphs is shown to exhibit at every temperature the mixing property known as Bernoullicity.

In this article, we derive an explicit formula for computing confidence interval for the mean of bounded random variables. In additional to its simplicity, the formula is very tight in comparison with existing results in literature.

The prevalence of implicit intergroup bias in adults underscores the importance of knowing when during development such biases are most amenable to change. Although research suggests that implicit intergroup bias undergoes little change across development, no studies have directly examined whether developmental differences exist in the capacity for novel implicit associations to form or change....

In this article an explicit method (relying on representation theory) to construct packings in Grassmannian space is presented. Infinite families of configurations having only one non-trivial set of principal angles are found using 2-transitive groups. These packings are proved to reach the simplex bound and are therefore optimal w.r.t. the chordal distance. The construction is illustrated by a...

Explicit expressions for the occupation time distribution of Brownian bridge, excursion and meander are derived using Kac’s formula and results of [4]. The first two distributions appeared in [8], and were derived using weak convergence of simple random walk.

We investigate the second-order correlation function of the characteristic polynomial of a sample covariance matrix. Starting from an explicit formula for a generating function, we re-obtain several well-known kernels from random matrix theory.

For Dyck paths (nonnegative symmetric) random walks, the location of the first maximum within the first sojourn is studied. Generating functions and explicit resp. asymptotic expressions for the average are derived. Related parameters are also discussed.

williams, watts, macleod and mathews' (1988) model of anxiety and depression leads to the prediction that anxious patients will show mood – congreuent implicit memory bias, while depressed patients will show mood-congruent explicit memory bias.although this prediction has been supported by some researchers (denny & hunt, 1992 mathews, moog, et al , 1989 watkins, et al, 1992), the reliabili...

We study statistical properties of zeros of random polynomials and random analytic functions associated with the pseudoeuclidean group of symmetries SU(1, 1), by utilizing both analytical and numerical techniques. We first show that zeros of the SU(1, 1) random polynomial of degree N are concentrated in a narrow annulus of the order of N around the unit circle on the complex plane, and we find ...

We derive optimal gambling and investment policies for cases in which the underlying stochastic process has parameter values that are unobserved random variables. For the objective of maximizing logarithmic utility when the underlying stochastic process is a simple random walk in a random environment, we show that a state-dependent control is optimal, which is a generalization of the celebrated...