arXiv subjects

Gabriel Raposo

Publications and source records attributed to Gabriel Raposo.

4 recordsLinked to original sources

arXiv2026

Circular Rearrangement Inequality and Optimal Cyclic Birth and Death Chains

We prove a generalized circular rearrangement inequality: among all circular arrangements of a finite collection of positive numbers, the greedy arrangement simultaneously maximizes the sums of products of $k$ consecutive entries for every $k$. This resolves a 2023 conjecture of Holmes-Holroyd-Ram\'irez and extends the classical circular rearrangement inequality for products of adjacent entries. As an application, we show that the greedy ordering minimizes the speed of a cyclic birth-and-death chain, resolving another conjecture of the same authors.

math.CO↗

arXiv2025

Global fluctuations for standard Young tableaux

We introduce the notion of a Young generating function for a probability measure on integer partitions. We use this object to characterize probability distributions over integer partitions satisfying a law of large numbers and those that satisfy a central limit theorem. We further establish a multilevel central limit theorem, which enables the study of random standard Young tableaux. As applications of these results, we describe the fluctuations of height functions associated with (i) the Plancherel growth process, (ii) random standard Young tableaux of fixed shape, and (iii) probability distributions induced by extreme characters of the infinite symmetric group $S_\infty$. In all cases, we identify the limiting fluctuations as a conditioned Gaussian Free Field.

math.PR↗

arXiv2022

A Detailed Proof of Pohst's Inequality

In 1977 Pohst conjectured a certain inequality for $n$ variables and give a computer-assisted proof for $n\leq 10$. We give a proof for all $n$ using a combinatorial argument. This inequality yields a better bound for the regulator in terms of the discriminant for totally real number fields.

math.NT↗

arXiv2022

A Refinement of Pohst's Inequality

We generalize an inequality conjectured by Pohst in 1977 and recently proved by the author and independently by Battistoni and Molteni. This new inequality improves a bound for the regulator in terms of the discriminant for totally real number fields by taking into account the signs of conjugates of the fundamental unit. We give a new interpretation to the problem and exploit the combinatorial method used by Pohst.

math.NT↗