Mauricio Duarte

activity

20122022

most citedA lower bound for the number of elastic collisions

10 citations · 15 across the 6 of their papers we have counts for

collaborators

9 papers

math.DS2022

Upper bound on the number of collisions of pinned billiard balls

Krzysztof Burdzy, Mauricio Duarte

We consider systems of "pinned balls," i.e., balls that have fixed positions and pseudo-velocities. Pseudo-velocities change according to the same rules as those for velocities of…

math-ph2021★ 4 cited

Fermi acceleration in rotating drums

Krzysztof Burdzy, Mauricio Duarte, Carl-Erik Gauthier +2

Consider hard balls in a bounded rotating drum. If there is no gravitation then there is no Fermi acceleration, i.e., the energy of the balls remains bounded forever. If there is g…

math.PR2020

Powers of Brownian Green Potentials

Claude Dellacherie, Mauricio Duarte, Servet Martínez +2

In this article we study stability properties of $g_{O}$ , the standard Green kernel for $O$ an open regular set in $R^{d}$ . In $d \geq 3$ we show that $g_{O}^{β}$ is again a Green kernel of…

math.DS2018★ 1 cited

On pinned billiard balls and foldings

Jayadev S. Athreya, Krzysztof Burdzy, Mauricio Duarte

We consider systems of "pinned balls," i.e., balls that have fixed positions and pseudo-velocities. Pseudo-velocities change according to the same rules as those for velocities of…

math.DS2018

On the number of hard ball collisions

Krzysztof Burdzy, Mauricio Duarte

We give a new and elementary proof that the number of elastic collisions of a finite number of balls in the Euclidean space is finite. We show that if there are $n$ balls of equal…

math.DS2018★ 10 cited

A lower bound for the number of elastic collisions

Krzysztof Burdzy, Mauricio Duarte

We prove by example that the number of elastic collisions of $n$ balls of equal mass and equal size in $d$ -dimensional space can be greater than $n^{3} /27$ for $n \geq 3$ and $d\geq 2…

math.PR2015

Gravitation versus Brownian motion

Sayan Banerjee, Krzysztof Burdzy, Mauricio Duarte

We investigate the motion of an inert (massive) particle being impinged from below by a particle performing (reflected) Brownian motion. The velocity of the inert particle increase…

math.PR2015

Asymptotics for the heat kernel in multicone domains

Pierre Collet, Mauricio Duarte, Servet Martinez +2

A multi cone domain $Ω \subseteq R^{n}$ is an open, connected set that resembles a finite collection of cones far away from the origin. We study the rate of decay in time of…

math.PR2012

Spinning Brownian motion

Mauricio A. Duarte

We prove strong existence and uniqueness for a reflection process $X$ in a smooth, bounded domain $D$ that behaves like obliquely-reflected-Brownian-motion, except that the directi…