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Lecturers
Stefano Olla stefano.olla@gssi.it
Lu Xu lu.xu@gssi.it
Anastasiia Trofimova anastasiia.trofimova@gssi.it
Timetable and workload
Lectures: 60 hours
Calendar: available at this link
Course description and outcomes
The aim of this course is to review the basic concepts in probability theory and stochastic processes, and to provide some mathematical methods for the study of statistical mechanics. We will also give the first introduction to the hydrodynamic limits for interacting particle systems.
An incomplete lecture note at this link
Course requirements
Basic functional analysis
Course content
1 Basic concepts in proability theory
2 Limit theorems (i.i.d. sequence, Law of Large Numbers, Central Limit Theorem)
3 Large deviations (Cramer's theorem)
4 Markov process with countable state space
5 Continuous-time martingale
6 Basic stochasitic analysis
7 Introduction to hydrodynamic limit (independent particles, simple exclusion process)
References
R. Durrett, Probability Theory and Examples
A. De Masi, E. Presutti, Mathematical Methods for Hydrodynamic Limits
C. Kipnis, C. Landim, Scaling Limits of Interacting Particle Systems
Examination and grading
Oral presentation on selected papers/books
Anonymous survey link: here.