# Seminars & Colloquia Calendar

## How does high-dimensional Euclidean space look when travelling on a cloud of uniformly random points?

#### Yuval Peres, BIMSA

Location: ** zoom**

Date & time: Wednesday, 29 March 2023 at 10:45AM - 11:45AM

Abstract: Approximating a high-dimensional lattice by a regular tree ("Bethe lattice") is a classical device in Math Physics. But how do we best approximate the local geometry of a random cloud of points in space? The answer is the Poisson-weighted infinite tree (PWIT), introduced by Aldous and Steel for a completely different purpose.

We exhibit the effectiveness of this approximation by analyzing the greedy matching of two independent Poisson processes in Euclidean space under an asymmetric color restriction. Blue points can only match to red points, while red points can match to points of either color. It is unknown if there exist intensities for the red and blue processes for which all points are matched. We prove that for any fixed intensities, there are unmatched blue points in sufficiently high dimension. Our proof uses greedy matching on the PWIT, which can be analyzed via differential equations. The proof is inspired by Aldous' 2002 proof of the zeta(2) limit for the random assignment problem, which was motivated by the heuristic cavity argument of Mezard-Parisi (1987).

(Joint work with Alexander Holroyd and James Martin.)

Chiara Damiolini, Ian Coley and Franco Rota -Charles Weibel Organizer's Page

Brooke Logan

Wujun Zhang Organizer's webpage

Ziming Shi, Sagun Chanillo, Xiaojun Huang, Chi Li, Jian Song Seminar website Old seminar website

Swastik Kopparty, Sepehr Assadi Seminar webpage

Jeffry Kahn, Bhargav Narayanan, Jinyoung Park Organizer's webpage

Brooke Ogrodnik, Website

Robert Dougherty-Bliss and Doron Zeilberger --> homepage

Paul Feehan, Daniel Ketover, Natasa Sesum Organizer's webpage

Lev Borisov, Emanuel Diaconescu, Angela Gibney, Nicolas Tarasca, and Chris Woodward Organizer's webpage

Jason Saied Seminar webpage

Brian Pinsky, Rashmika Goswami website

Quentin Dubroff Organizer's webpage

James Holland; Organizer website

Edna Jones Organizer's webpage

Brooke Ogrodnik website

Yanyan Li, Zheng-Chao Han, Jian Song, Natasa Sesum Organizer's Webpage

Organizer: Luochen Zhao

Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song Organizer's Page

Lisa Carbone, Yi-Zhi Huang, James Lepowsky, Siddhartha Sahi Organizer's webpage

Simon Thomas website

Kasper Larsen, Daniel Ocone and Kim Weston Organizer's page

Joel Lebowitz, Michael Kiessling

Yanyan Li, Haim Brezis Organizer's Webpage

Stephen D. Miller, John C. Miller, Alex V. Kontorovich, Alex Walker seminar website

Stephen D. Miller

Brooke Ogrodnik, Website

Organizers: Yanyan Li, Z.C. Han, Jian Song, Natasa Sesum

Yael Davidov Seminar webpage

Kristen Hendricks, Xiaochun Rong, Hongbin Sun, Chenxi Wu Organizer's page

Fioralba Cakoni Seminar webpage

Ebru Toprak, Organizer

- Show events from all categories

## Special Note to All Travelers

Directions: map and driving directions. If you need information on public transportation, you may want to check the New Jersey Transit page.

*Unfortunately, cancellations do occur from time to time. Feel free to call our department: 848-445-6969 before embarking on your journey. Thank you.*