PROBABILISTIC METHODS IN MATHEMATICAL PHYSICS

Degree course: 
Corso di First cycle degree in MATHEMATICS
Academic year when starting the degree: 
2015/2016
Year: 
3
Academic year in which the course will be held: 
2017/2018
Course type: 
Compulsory subjects, characteristic of the class
Credits: 
8
Period: 
First Semester
Standard lectures hours: 
64
Detail of lecture’s hours: 
Lesson (64 hours)
Requirements: 

Lebesgue integration theory, probability theory

Final Examination: 
Orale

Oral examination

Assessment: 
Voto Finale

Provide an introduction to sequences of I.I.D. random variables and Markov chains

Independent and identically distributed random variables. The Central Limit Theorem. Markov chains. Homogeneous Markov chains. Random walks on groups. Recurrence and transience. Polya’s theorem on randon walks in the n-dimensional integer lattice. Random walks and the discrete heat equation

1. Lecture notes
2. Y.G. Sinai, Theory of Probability and Random Processes, Springer

Frontal lessons