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Probability and Mathematics of Phase Transitions I - NTMF027

Title:	Pravděpodobnost a matematika fázových přechodů I
Guaranteed by:	Institute of Theoretical Physics (32-UTF)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2020
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time
Additional information:	http://utf.mff.cuni.cz/vyuka/NTMF027

Guarantor:	doc. RNDr. Miloš Zahradník, CSc.
Classification:	Physics > Theoretical and Math. Physics
Is co-requisite for:	NTMF047

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

Last update: T_UTF (16.05.2003)

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.

Course completion requirements - Czech

Last update: doc. RNDr. Karel Houfek, Ph.D. (11.06.2019)

Ústní zkouška

Requirements to the exam - Czech

Last update: doc. RNDr. Miloš Zahradník, CSc. (13.10.2017)

Zkouška bude ústní, po předběžné domluvě studenta s přednášejícím půjde o rozvinutí některého z témat na přednášce probraných

Syllabus -

Last update: T_UTF (16.05.2003)

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.