Syllabus
0 Elements of measure theory, products and convolutions of measures. Central limit theorem for multiple convolutions. 1 Introduction to probability theory. 2 Gaussian measures in finite dimensions. 3 Independence, Markov chains. 4 Random walks, Feynman-Kac formula for discrete Laplacian. 5 Translation invariant quadratic forms, their potential theory and Gaussian measures. 6 Elements of large deviations. 7 Entropy. 8 Introduction to random graphs. 9 Introduction to percolation.
Annotation
This two semestral course is devoted to some basic notions and merhods of probability theory and mathematical statistical physics. Special emphasis is given to the applications of contour methods in Ising-type systems. For the 3rd and 4th year of the TF study, mainly for students of mathematics and physics.
Requirements: a good knowledge of basic course of mathematics for physicists.