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401-4604-DRL 2 Credits DR D-MATH

First Passage Percolation and Large Deviations

Lecturers & Examiners: Dr. Barbara Dembin

Only for ETH D-MATH doctoral students and for doctoral students from the Institute of Mathematics at UZH. The latter need to send an email to Jessica Bolsinger ( ) with the course number. The email should have the subject „Graduate course registration (ETH)“.

VVZ CR n/a

Last Updated: 2026-02-05 16:22:18

Abstract

Keywords : First passage percolation; large deviations; concentration inequalities; noise sensitivity; fluctuations

Objective

The model of first passage percolation (FPP) was introduced in 1965 by Hammersley and Welsh to study the spread of a fluid through a random medium. The model is defined on the lattice (Z^d,E^d) by assigning independently to each edge a positive random variable representing the time to cross the edge. This induces a random metric on the lattice, where the time between two vertices corresponds to the time of the shortest path. In this course, our goal is to study the asymptotic properties of this random metric, as well as the time-minimizing paths (geodesics). In particular, we will study time and spatial fluctuations of geodesics. The objectives of this class are two-fold. First, discover an active field of research, have an overview of recent results and major open questions. Second, get familiar with various tools and concepts of probability that are not specific to this model. In particular, this class will contain an introduction to large deviations theory.

Resources

Literature

50 Years of First-Passage Percolation, Auffinger, Damron, Hanson Aspects of first passage percolation, Kesten

General Information

Language: English
Levels: DR

Examination

Type: ungraded semester performance

Registration & Places

Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type	Title	Time & Place	Hours
lecture	First Passage Percolation and Large Deviations	Mon 12:15-14:00 (HG D 1.1)	2 h weekly

Offered In

Doctorate Mathematics (More Information at: )
- Subject Specialisation (The list of courses (together with the allocated credit points) eligible for doctoral students is published each semester in the newsletter of the ZGSM.)
  - Graduate School (Official website of the Zurich Graduate School in Mathematics: )