Math Courses

PILLAR Course: Probability and Statistical Mechanics

Europe/Rome
Description

Lecturers
Stefano Olla stefano.olla@gssi.it
Lu Xu lu.xu@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. 

Course requirements
Basic functional analysis

Course content
1 Basic concepts in probability theory
2 Law of Large Numbers and Central Limit Theorem
3 Markov process with countable state space
4 Discrete and continuous-time martingales
5 Basic stochastic analysis and stochastic differential equation
6 Large Deviation Theory

References
R. Durrett, Probability Theory and Examples
I. Karatzas, S. E. Shreve, Brownian Motion and Stochastic Calculus

Examination and grading
Written and/or oral exam