We describe a new algorithm for the perfect simulation of variable length Markov chains and random systems with perfect connections. This algorithm, which generalizes Propp and Wilson's simulation scheme, is based on the idea of coupling into and from ...

In this article, the moments of nearest neighbor distance distributions are examined. While the asymptotic form of such moments is well-known, the boundary effect has this far resisted a rigorous analysis. Our goal is to develop a new technique that ...

We present a randomized approximation algorithm for counting contingency tables, m × n non-negative integer matrices with given row sums R = (r₁,…,r_m) and column sums C = (c₁,…,c_n). We define smooth margins (R,C) in terms of the typical table and prove ...

We consider the problem of generating a coloring of the random graph 𝔾_n,p uniformly at random using a natural Markov chain algorithm: the Glauber dynamics. We assume that there are βΔ colors available, where Δ is the maximum degree of the graph, and we ...

We consider the Hamiltonian cycle problem embedded in singularly perturbed (controlled) Markov chains. We also consider a functional on the space of stationary policies of the process that consists of the (1,1)-entry of the fundamental matrices of the ...

We continue our analysis of the number partitioning problem with n weights chosen i.i.d. from some fixed probability distribution with density ρ. In Part I of this work, we established the so-called local REM conjecture of Bauke, Franz and Mertens. ...

In this article we consider the number partitioning problem (NPP) in the following probabilistic version: Given n numbers X₁,…,X_n drawn i.i.d. from some distribution, one is asked to find the partition into two subsets such that the sum of the numbers ...

We study the largest component of a random (multi)graph on n vertices with a given degree sequence. We let n → ∞. Then, under some regularity conditions on the degree sequences, we give conditions on the asymptotic shape of the degree sequence that ...

Given a homogeneous Poisson point process in ℝ^d, Häggström and Meester (Random Struct Algorithms 9 (1996) 295315) asked whether it is possible to place spheres (of differing radii) centred at the points, in a translation-invariant way, so that the spheres ...

In this article, we continue the combinatorial study of models of particles jumping on a row of cells which we initiated with the standard totally asymmetric simple exclusion process or TASEP (Duchi and Schaeffer, Journal of Combinatorial Theory, Series ...

We consider a type of dependent percolation introduced in [2], where it is shown that certain “enhancements” of independent (Bernoulli) percolation, called essential, make the percolation critical probability strictly smaller. In this study we first ...

Let L be chosen uniformly at random from among the latin squares of order n ≥ 4 and let r,s be arbitrary distinct rows of L. We study the distribution of σ_r,s, the permutation of the symbols of L which maps r to s. We show that for any constant c > 0, the ...

Caching is widely recognized as an effective mechanism for improving the performance of the World Wide Web. One of the key components in engineering the Web caching systems is designing document placement-replacement algorithms for updating the ...

Let 𝒞 be a class of distributions over Bⁿ. A deterministic randomness extractor for 𝒞 is a function E : BⁿarB^m such that for any X in 𝒞 the distribution E(X) is statistically close to the uniform distribution. A long line of research deals with ...

Monte Carlo algorithms typically need to generate random variates from a probability distribution described by an unnormalized density or probability mass function. Perfect simulation algorithms generate random variates exactly from these distributions, ...

Let I be a random 3CNF formula generated by choosing a truth assignment φ for variables x₁, x_n uniformly at random and including every clause with i literals set true by φ with probability p_i, independently. We show that for any constants 0 ≤ η₂,η₃ ≤ 1 ...

Zhang found a simple, elegant argument deducing the nonexistence of an infinite open cluster in certain lattice percolation models (for example, p = 1-2 bond percolation on the square lattice) from general results on the uniqueness of an infinite open ...

We extend results about heights of random trees (Devroye, JACM [33 (1986) 489–498], SIAM J COMP [28 (1998) 409–432)]. In this paper, a general split tree model is considered in which the normalized subtree sizes of nodes converge in distribution. The ...

For a subset $\cal{S}$ of positive integers let ©(n,$\cal{S}$) be the set of partitions of n into summands that are elements of $\cal{S}$. For every λ ε Ω(n,$\cal{S}$), let M_n(λ) be the number of parts, with multiplicity, that λ has. Put a uniform ...

In a recent breakthrough, [Bshouty et al., J Comput Syst Sci 71 (2005), 250265] obtained the first passive-learning algorithm for DNFs under the uniform distribution. They showed that DNFs are learnable in the Random Walk and Noise Sensitivity models. We ...