arXiv subjects

Nadya Nabahi

Publications and source records attributed to Nadya Nabahi.

2 recordsLinked to original sources

arXiv2026

Interface between competing random walks on a cycle

We consider a competition between two independent random walks on a cycle of length $N$. Each vertex is claimed by the walker that visits it first, and remains claimed thereafter. We prove that if the initial distance between the walkers is $d$, then the expected number of edges whose endpoints are claimed by different walkers is of order $\ln(1+N/d).$ This confirms the logarithmic dependence on $N/d$ predicted in Gomes Jr. et al. [Coloring of a one-dimensional lattice by two independent random walkers. Physica A: Statistical Mechanics and its Applications 225.1 (1996): 81-88].

math.PR↗

arXiv2025

Easy estimates of Lyapunov exponents for random products of matrices

The problems that we consider in this paper are as follows. Let $A_1, \ldots, A_k$ be square matrices (over reals). Let $W=w(A_1, \ldots, A_k)$ be a random product of $n$ matrices. What is the expected growth rate of the largest (in the absolute value) entry in such a random product? What is the (maximal) Lyapunov exponent for a random matrix product like that? We give an answer to the first question under some mild restrictions on the entries of $A_i$. For the second question, we offer a very simple and efficient method to produce an upper bound on the Lyapunov exponent.

math.GR↗