2nd degree (Master)
Prof. Jonathan Breuer
Coordinator Office Hours:
Prof Yoram Last
Szego's Theorems deal with the asymptotics of Toeplitz determinants and are of central importance in various areas of analysis. The course will survey several proofs of the two theorems and in particular various applications in random matrix theory, statistical mechanics, orthogonal polynomials and spectral theory.
To study Szego's Theorems, their proofs and some of their applications.
Learning outcomes - On successful completion of this module, students should be able to:
to quote Szego's Theorems, to prove them and to describe applications.
Teaching arrangement and method of instruction:
1) Szego's Theorems and orthogonal polynomials.
2) The Law of Large Numbers and Central Limit Theorem in Random Matrix Theory.
3) Szego's Theorem and spectral stability.
4) Szego's Theorem and the Ising model.
Additional Reading Material:
End of year written/oral examination 0 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 100 %
Assignments 0 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 0 %