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401-4604-23L 4 Credits MSC D-MATH

First Passage Percolation and Large Deviations

Lecturers & Examiners: Dr. Barbara Dembin
VVZ CR n/a

Last Updated: 2026-02-05 16:22:14

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
MSC

Examination

Type
session examination
Mode
oral 20 minutes

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