Ludovick Bouthat

activity

20212026

p

-norm of

A_{s}

and

C

-matrices

6 citations · 23 across the 18 of their papers we have counts for

collaborators

19 papers

math.CV2026

A proof of Borcea's quadratic variance conjecture

Ludovick Bouthat, Shaun Fallat

Let $p$ be a complex polynomial of degree $n \geq 2$ , and let $σ_{2} (p)$ be the root mean square distance of its zeros from their centroid, including multiplicities. We prove that every…

math.CV2026

The sharp constant in the Mashreghi-Ransford inequality

Ludovick Bouthat

Let $(a_{n})_{n \geq 0}$ be a sequence of complex numbers, and define \[ b_n=\sum_{k=0}^n \binom{n}{k} a_k, \qquad c_n=\sum_{k=0}^n \binom{n}{k}(-1)^{n-k}a_k. \] Let $β > 1$ , put $α=\sqr…

math.CA2026

A Finite-order Characterization of Entrywise Positivity Preservers

Ludovick Bouthat, Dominique Guillot

Fix $I = (0, ρ)$ , where $0 < ρ \leq \infty$ , and let $P_{n} (I)$ be the set of positive semidefinite $n \times n$ matrices with entries in $I$ . A longstanding problem in matrix the…

math.FA2026

Norm of infinite doubly stochastic matrices

Ludovick Bouthat, Javad Mashreghi, Raphaël Vo

In finite dimensions, every doubly stochastic matrix has the $ℓ^{p}$ -operator norm equal to $1$ for all $1 \leq p \leq \infty$ . However, in the infinite-dimensional setting, this pr…

math.PR2026

On the convergence of doubly stochastic Markov chains

Ludovick Bouthat, Nicolas Doyon, Javad Mashreghi +1

We characterize the asymptotic behavior of time-homogeneous doubly stochastic Markov chains. Our investigation revolves around understanding the dynamics of products of doubly stoc…

math.CA2026

Weighted Hardy Inequalities for Nested Averages

Ludovick Bouthat, Pierre-Olivier Parisé

We study a family of Hardy-type inequalities for weighted averages over nested subsets of a measure space. Given a partition of a measure space and a weight function $m$ , we consid…

math.MG2026

Sharp Inequalities for Products of Principal Minors of Positive Definite Matrices

Tobias Boege, Ludovick Bouthat

We study sharp inequalities for ratios of products of principal minors of real positive definite matrices. Our main result gives a closed-form solution to a family of nonconvex opt…

math.CO2026

A general framework for inequalities on simple graphs

Ludovick Bouthat, Ángel Chávez, Sam Sheng

A general framework is developed for deriving sharp inequalities on simple graphs from majorization and Schur-convexity. After establishing majorization relations between the spect…

math.NA2026

Convergence Analysis of the Random Bisection Method

Ludovick Bouthat, Philippe-André Luneau, Philippe Petitclerc

We propose a generalized version of the bisection method where the cutting point between the two subintervals is chosen at random following an arbitrary distribution. We compute ex…

math.CO2025

Number of orbits of $k$ -subsets of permutations

Ludovick Bouthat, Raghavendra Tripathi

Let $S_{n}$ denote the symmetric group of order $n$ . Say that two subsets $x, y \subseteq S_{n}$ are \emph{equivalent} if there exist permutations $g_{1}, g_{2} \in S_{n}$ such that $g_1xg_2=y…

math.FA2024

Hunter's positivity theorem and random vector norms

Ludovick Bouthat, Ángel Chávez, Stephan Ramon Garcia

A theorem of Hunter ensures that the complete homogeneous symmetric polynomials of even degree are positive definite functions. A probabilistic interpretation of Hunter's theorem s…

math.MG2024★ 1 cited

On the Submultiplicativity of Matrix Norms Induced by Random Vectors

Ludovick Bouthat

In a recent article, Chávez, Garcia and Hurley introduced a new family of norms $∥ \cdot ∥_{X, d}$ on the space of $n \times n$ complex matrices which are induced by random…

math.CA2023

On the monotonicity of left and right Riemann sums

Ludovick Bouthat

Riemann sums, a classical method for approximating the definite integral of a function, have been extensively studied in the past. However, their monotonic properties, while still…

math.MG2023★ 2 cited

On the Geometry of the Birkhoff Polytope. II. The Schatten $p$ -norms

Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin

In the first of this series of two articles, we studied some geometrical aspects of the Birkhoff polytope, the compact convex set of all $n \times n$ doubly stochastic matrices, na…

math.MG2023★ 4 cited

On the Geometry of the Birkhoff Polytope. I. The operator $ℓ_{n}^{p}$ -norms

Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin

The geometry of the Birkhoff polytope, i.e., the compact convex set of all $n \times n$ doubly stochastic matrices, has been an active subject of research. While its faces, edges a…

math.FA2023

Weighted averages of $ℓ^{p}$ sequences

Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin

The objective of the present paper is to establish three Hardy-type inequalities in which the arithmetic mean over a sequence of non-negative real numbers is replaced by some weigh…

math.MG2023★ 4 cited

On a question of Erdős on doubly stochastic matrices

Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin

In a celebrated paper of Marcus and Ree (1959), it was shown that if $A = [a_{ij}]$ is an $n \times n$ doubly stochastic matrix, then there is a permutation $σ \in S_{n}$ such that $\su…

math.FA2021★ 6 cited

The $p$ -norm of circulant matrices

Ludovick Bouthat, Apoorva Khare, Javad Mashreghi +1

In this note we study the induced $p$ -norm of circulant matrices $A (n, \pm a, b)$ , acting as operators on the Euclidean space $R^{n}$ . For circulant matrices whose entries ar…

math.FA2021★ 6 cited

The critical point and the $p$ -norm of $A_{s}$ and $C$ -matrices

Ludovick Bouthat, Javad Mashreghi

The $L$ -matrix $A_{s} = [1/ (n + s)]$ was introduced in \cite{MRtmp}. As a surprising property, we showed that its 2-norm is constant for $s \geq s_{0}$ , where the critical point $s_{0}$ is u…

A proof of Borcea's quadratic variance conjecture

The sharp constant in the Mashreghi-Ransford inequality

A Finite-order Characterization of Entrywise Positivity Preservers

Norm of infinite doubly stochastic matrices

On the convergence of doubly stochastic Markov chains

Weighted Hardy Inequalities for Nested Averages

Sharp Inequalities for Products of Principal Minors of Positive Definite Matrices

A general framework for inequalities on simple graphs

Convergence Analysis of the Random Bisection Method

Number of orbits of k-subsets of permutations

Hunter's positivity theorem and random vector norms

On the Submultiplicativity of Matrix Norms Induced by Random Vectors

On the monotonicity of left and right Riemann sums

On the Geometry of the Birkhoff Polytope. II. The Schatten p-norms

On the Geometry of the Birkhoff Polytope. I. The operator ℓnp​-norms

Weighted averages of ℓp sequences

On a question of Erdős on doubly stochastic matrices

The p-norm of circulant matrices

The critical point and the p-norm of As​ and C-matrices

Number of orbits of $k$ -subsets of permutations

On the Geometry of the Birkhoff Polytope. II. The Schatten $p$ -norms

On the Geometry of the Birkhoff Polytope. I. The operator $ℓ_{n}^{p}$ -norms

Weighted averages of $ℓ^{p}$ sequences

The $p$ -norm of circulant matrices

The critical point and the $p$ -norm of $A_{s}$ and $C$ -matrices