We consider several aspects of the scaling limit of percolation on random planar triangulations, both finite and infinite. The equivalents for random maps of Cardy’s formula for the limit under scaling of various crossing probabilities are given. The limit probabilities are expressed in terms of simple events regarding Airy-Lévy processes. Some explicit formulas for limit probabilities follow f...

Explicit expressions are derived for derivatives at zero lag of the mean-square prediction error for a class of random processes that includes those with rational power spectra. A simple random process not in the class is demonstrated. A sufficient condition for membership in the class is given.

In this note we study, for a random lattice L of large dimension n, the supremum of the real parts of the zeros of the Epstein zeta function En(L, s) and prove that this random variable has a limit distribution, which we give explicitly. This limit distribution is studied in some detail; in particular we give an explicit formula for its distribution function.

We study right tail large deviations of the logarithm of the partition function for directed lattice paths in i.i.d. random potentials. The main purpose is the derivation of explicit formulas for the 1+1-dimensional exactly solvable case with log-gamma distributed random weights. Along the way we establish some regularity results for this rate function for general distributions in arbitrary dim...

To investigate the fundamental causes of bloat, six artificial random binary tree search spaces are presented. Fitness is given by program syntax (the genetic programming genotype). GP populations are evolved on both random problems and problems with “building blocks”. These are compared to problems with explicit ineffective code (introns, junk code, inviable code). Our results suggest the entr...

Over the last few years, the realm of foreign language learning has witnessed an abundance of research concerning the effectiveness of corrective feedback on the acquisition of grammatical features, with the study of other target language subsystems, such as pronunciation, being few and far between. In order to bridge this gap, the present study intended to investigate and compare the immediate...

We introduced a random vector , where has Poisson distribution and are minimum of independent and identically distributed exponential random variables. We present fundamental properties of this vector such as PDF, CDF and stochastic representations. Our results include explicit formulas for marginal and conditional distributions, moments and moments generating functions. We also derive moments ...

This paper states a law of large numbers for a random walk in a random iid environment on Z d , where the environment follows some Dirichlet distribution. Moreover, we give explicit bounds for the asymptotic velocity of the process and also an asymptotic expansion of this velocity at low disorder.

In the random deletion channel, each bit is deleted independently with probability p. For the random deletion channel, the existence of codes of rate (1− p)/9, and thus bounded away from 0 for any p < 1, has been known. We give an explicit constructionwith polynomial time encoding and deletion correction algorithms with rate c0(1 − p) for an absolute constant c0 > 0.

We propose a simple, direct approach for computing the expected cost of random partial match queries in random quadtrees. The approach gives not only an explicit expression for the leading constant in the asymptotic approximation of the expected cost but also more terms in the asymptotic expansion if desired.