SHORT Course: Hydrodynamic limits: from interacting particle systems to hyperbolic conservation laws

Monday 18 May 2026, 09:00 → Friday 5 Jun 2026, 09:00 Europe/Rome

GSSI

Lecturer
Lu Xu lu.xu@gssi.it 

Timetable and workload
Lectures: 16 hours

Course content
This course develops the mathematical theory that connects microscopic interacting particle systems with macroscopic hyperbolic PDEs. Focusing on the systems with a single conserved quantity, we derive nonlinear (quasi-linear) scalar conservation law under the hyperbolic space-time scale. We study the emergence of entropy conditions from random particle interactions using both probablistic and analytic tools: attractiveness, Young measures, and the entropy method.
Topics include:

• Asymmetric attractive process (typical examples are the exclusion process and the misanthrope process)
• Review of entropy solutions and measure-valued entropy solutions
• Empirical Young measures
• Attractiveness
• Replacement lemma and the entrioy method
• Microscopic entropy inequality

If time permits, we also discuss the formulation of boundary layers in boundary-driven dynamics.

Reference
Kipnis, Landim, Scaling limits of Interacting Particle Systems (mainly Chapter 8)