arXiv subjects

Elahe Zohoorian Azad

Publications and source records attributed to Elahe Zohoorian Azad.

5 recordsLinked to original sources

arXiv2021

Asymptotic behavior of some factorizations of random words

In this paper we consider the normalized lengths of the factors of some factorizations of random words. First, for the \emph{Lyndon factorization} of finite random words with $n$ independent letters drawn from a finite or infinite totally ordered alphabet according to a general probability distribution, we prove that the limit law of the normalized lengths of the smallest Lyndon factors is a variant of the stickbreaking process. Convergence of the distribution of the lengths of the longest factors to a Poisson-Dirichlet distribution follows. Secondly we consider the \emph{standard factorization} of random \emph{Lyndon word} : we prove that the distribution of the normalized length of the standard right factor of a random $n$-letters long Lyndon word, derived from such an alphabet, converges, when $n$ is large, to: $$μ(dx)=p_1 δ_{1}(dx) + (1-p_1) \mathbf{1}_{[0,1)}(x)dx,$$ in which $p_1$ denotes the probability of the smallest letter of the alphabet.

math.PR↗

arXiv2012

Asymptotic cost of cutting down random free trees

The limit distribution of the total cost incurred by splitting a tree uniformly distributed on the set of all finite free trees, appears as an additive functional induced by a toll equal to the square of the size of tree. The main tools used are the recent results connecting the asymptotics of generating functions with the asymptotics of their Hadamard product, and the method of moments.

math.PR↗

arXiv2012

Positions of the ranks of factors in certain finite long length words

We consider the set of finite random words $\mathcal A^\star$, with independent letters drawn from a finite or infinite totally ordered alphabet according to a general probability distribution. On a specific subset of $\mathcal A^\star$, considering certain factorization of the words which are labelled with the ranks, base on the lexicographical order, we prove that the normalized position of the ranks of factors, are uniform, when the length of the word goes to infinity.

math.PR↗

arXiv2010

Asymptotic Analysis of a Drop-Push Model For Percolation

In this article, we study a type of a one dimensional percolation model whose basic features include a sequential dropping of particles on a substrate followed by their transport via a pushing mechanism (see [S. N. Majumdar and D. S. Dean, Phys. Rev. Ltt. A 11, 89 (2002)]). Consider an empty one dimensional lattice with n empty sites and periodic boundary conditions (as a necklace with n rings). Imagine then the particles which drop sequentially on this lattice, uniformly at random on one of the n sites. Letting a site can settles at most one particle, if a particle drops on an empty site, it stick there and otherwise the particle moves according to a symmetric random walk until it takes place in the first empty site it meet. We study here, the asymptotic behavior of the arrangement of empty sites and of the total displacement of all particles as well as the partial displacement of some particles.

math.PR↗

arXiv2004

Limit law of the standard right factor of a random Lyndon word

Consider the set of finite words on a totally ordered alphabet with $q$ letters. We prove that the distribution of the length of the standard right factor of a random Lyndon word with length $n$, divided by $n$, converges to: $$μ(dx)=\frac1q δ_{1}(dx) + \frac{q-1}q \mathbf{1}_{[0,1)}(x)dx,$$ when $n$ goes to infinity. The convergence of all moments follows. This paper completes thus the results of \cite{Bassino}, giving the asymptotics of the mean length of the standard right factor of a random Lyndon word with length $n$ in the case of a two letters alphabet.

math.PR↗