Directed last passage percolation: analytic and integrable aspects

Schedule

Tuesday: 15h45 - 17h45

Friday : 13h30 - 15h30

Plan

Lectures notes (very incomplete, in progress, use as a summary)

Class 0 - On continuous time Markov processes

Class 1 - Definition of equivalent particle systems and growth processes

Analytic aspects

Class 2 - Shape theorem

Class 3 - Finiteness criterion for the shape

Class 4 - Fluctuations at worse of N^\half via measure concentration

Class 5 - Proof of Talagrand's inequality

Integrable aspects

Class 6 - Combinatorics of Young tableaux

Class 7 - Formulae for Schur functions

Class 8 - The RSK correspondence

Class 9 - C. Greene's Lemma

Class 10 - From Okounkov's determinality to the Tracy-Widom distribution

Class 11 - Asymptotic analysis of kernels

Extra material

Last year's exam

Last year's exercises

Out of scope

Hydrodynamics following the book "Scaling Limits of Interacting Particle Systems" by Kipnis and Landim.