With any hypothesis class one can associate a bipartite graph whose vertices are the hypotheses H on one side and all possible labeled examples X on the other side, and an hypothesis is connected to all the labeled examples that are consistent with it. We call this graph the hypotheses graph. We prove that any hypothesis class whose hypotheses graph is mixing cannot be learned using less than 2...

We consider small random perturbations of a large class of nonuniformly hy-perbolic unimodal maps and prove stochastic stability in the strong sense (L 1-convergence of invariant densities) and uniform bounds for the exponential rate of decay of correlations. Our method is based on an analysis of the spectrum of a modiied Perron-Frobenius operator for a tower extension of the Markov chain.

Approximate counting via correlation decay is the core algorithmic technique used in the sharp delineation of the computational phase transition that arises in the approximation of the partition function of anti-ferromagnetic two-spin models. Previous analyses of correlation-decay algorithms implicitly depended on the occurrence of strong spatial mixing. This, roughly, means that one uses worst...

The theorem of Shannon-McMillan-Breiman states that for every generating partition on an ergodic system, the exponential decay rate of the measure of cylinder sets equals the metric entropy almost everywhere (provided the entropy is finite). In this paper we prove that the measure of cylinder sets are lognormally distributed for strongly mixing systems and infinite partitions and show that the ...

We argue that there could be large, SU(3) violating resonance contributions to D → Kπ decays which would affect the extraction of the D0 −D0 mixing parameters from experiment. Such contributions can induce a large strong phase in the interference between the doubly Cabibbo suppressed and the mixing induced Cabibbo favored contributions to the D0 → K+π− and D0 → K−π+ decays. Consequently, the in...

For a strictly stationary sequence of random vectors in R we study convergence of partial sums processes to Lévy stable process in the Skorohod space with J1-topology. We identify necessary and sufficient conditions for such convergence and provide sufficient conditions when the stationary sequence is strongly mixing.

1.2 Relating the inverse and standard shuffles We now need to relate ∆(t) to ∆(t). We will do this by taking a more general view of shuffles. We will think of a shuffle as a random walk on the symmetric group Sn. The walk is defined by a set of generators G = {g1, . . . , gk} and a probability distribution P over G. (At each step of the walk, we pick a random gi according to P and apply gi to t...

The remarkable contribution by Weitz gives a general framework to establish the strong spatial mixing property of Gibbs measures. In light of Weitz’s work, we prove the strong spatial mixing for binary Markov random fields under the condition that the ‘external field’ is uniformly large or small by turning them into a corresponding Ising model. Our proof is done through a ‘path’ characterizatio...

Given some regularity conditions on the distribution F(.) of a random sample X h ..., Xn emanating from a strictly stationary sequence of random variables satisfying a strong mixing condition, it is shown that the sequence of quantile processes {n1hf(F1(s))(F;1(s)-F1(s)); 0 < s < I} behaves like a sequence of Brownian bridges {BD(s); 0 < s < I}. The latter is then utilized to construct (i) simu...