arXiv subjects

Majid Salamat

Publications and source records attributed to Majid Salamat.

3 recordsLinked to original sources

arXiv2026

On the Dimension of the Best-Worst Choice Polytope

For a set of $n$ alternatives, the best--worst choice polytope is the convex hull of the deterministic best--worst choice vectors induced by all linear rankings of the alternatives. The question of determining the dimension of this polytope as a function of $n$ has been raised by Doignon \cite{Doignon2023}. In this paper we answer this question by finding an explicit formula for this dimension. Our proof is motivated by a representation-theoretic interpretation of the relevant rank problem for the symmetric group, but is presented entirely in elementary linear-algebraic terms. The connection with representation theory will be explored elsewhere.

math.CO↗

arXiv2020

Limit theorems for integral functionals of Hermite-driven processes

Consider a moving average process $X$ of the form $X(t)=\int_{-\infty}^t x(t-u)dZ_u$, $t\geq 0$, where $Z$ is a (non Gaussian) Hermite process of order $q\geq 2$ and $x:\mathbb{R}_+\to\mathbb{R}$ is sufficiently integrable. This paper investigates the fluctuations, as $T\to\infty$, of integral functionals of the form $t\mapsto \int_0^{Tt }P(X(s))ds$, in the case where $P$ is any given polynomial function. It extends a study initiated in Tran (2018), where only the quadratic case $P(x)=x^2$ and the convergence in the sense of finite-dimensional distributions were considered.

math.PR↗

arXiv2015

The general recombination equation in continuous time and its solution

The process of recombination in population genetics, in its deterministic limit, leads to a nonlinear ODE in the Banach space of finite measures on a locally compact product space. It has an embedding into a larger family of nonlinear ODEs that permits a systematic analysis with lattice-theoretic methods for general partitions of finite sets. We discuss this type of system, reduce it to an equivalent finite-dimensional nonlinear problem, and establish a connection with an ancestral partitioning process, backward in time. We solve the finite-dimensional problem recursively for generic sets of parameters and briefly discuss the singular cases, and how to extend the solution to this situation.

math.CA↗