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ANALYTIC AND PROBABILISTIC METHODS IN MATHEMATICAL PHYSICS A

Degree course: 
Corso di Second cycle degree in MATHEMATICS
Academic year when starting the degree: 
2023/2024
Year: 
1
Academic year in which the course will be held: 
2023/2024
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: 

basics of probability theory

Final Examination: 
Orale

Oral test which consists in verifying the ability to express oneself in correct mathematical language and to demonstrate some of the theorems encountered during the course.

Assessment: 
Voto Finale

The aim of the course is to provide students with the basic theoretical tools of the theory of discrete-time stochastic processes, including applications to Markov chains.
The result to be achieved at the end of the course is that the student knows how to use the basic techniques of the theory of stochastic processes, having also developed a good intuition on the meaning of the concepts learned.

Basics of the abstract theory of measure. Independent and identically distributed random variables. Markov chains. Homogeneous Markov chains. Random walks on groups. Recurrence and transience. Polya’s theorem on randon walks in the n-dimensional integer lattice. Stationary processes, the ergodic theorem, Poincaré recurrence. Irreducible Markov chains and ergodicity.

Basics of the abstract theory of measure. Independent and identically distributed random variables. Markov chains. Homogeneous Markov chains. Random walks on groups. Recurrence and transience. Polya’s theorem on randon walks in the n-dimensional integer lattice. Stationary processes, the ergodic theorem, Poincaré recurrence. Irreducible Markov chains and ergodicity.

Convenzionale

Frontal lessons: 64 hours. In the lectures the theoretical notions are developed and the techniques necessary for the application of the theory to the solution of problems in Mathematical Physics are described.

to make an appointment write to posilicano@uninsubria.it

Professors

POSILICANO ANDREA

Borrowers