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Course, academic year 2018/2019
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Interacting Particle Systems - NMTP612
Title in English: Systémy částic
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2018
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: Jan Swart, Dr.
Class: Pravděp. a statistika, ekonometrie a fin. mat.
M Mgr. PMSE
M Mgr. PMSE > Volitelné
Classification: Mathematics > Probability and Statistics
Annotation -
Last update: T_KPMS (27.04.2016)
Interacting particle systems are collections of locally interacting Markov processes, situated on a lattice. While the process at a single lattice point is usually a very simple, finite state Markov process, the interaction between neighbours causes the system as a whole to show interesting behaviour, such as phase transitions. The study of interacting particle systems started in the early 1970-ies motivated by problems from theoretical physics. Since that time, the field underwent a growth, with links to and applications in many other fields of science. For PhD students.
Aim of the course -
Last update: T_KPMS (07.05.2014)

A first introduction to the theory of interacting particle systems.

Course completion requirements -
Last update: Jan Swart, Dr. (13.02.2019)

Written exam.

Literature - Czech
Last update: T_KPMS (07.05.2014)

Základní:

J.M. Swart: Lecture Notes Interacting Particle Systems.

http://staff.utia.cas.cz/swart/cztea_index.html

Doporučená:

T.M.~Liggett.

Interacting Particle Systems.

Springer-Verlag, New York, 1985.

R. Durrett.

Lecture notes on particle systems and percolation.

Wadsworth & Brooks/Cole, Pacific Grove, 1988.

T.M. Liggett.

Stochastic interacting systems: contact, voter and exclusion processes.

Springer-Verlag, Berlin, 1999.

Teaching methods -
Last update: T_KPMS (07.05.2014)

Lecture.

Syllabus -
Last update: T_KPMS (07.05.2014)

Interacting particle systems, contact process, voter model, Ising

model, exclusion process, mean-field model, duality, invariant

measure, phase transition.

Entry requirements -
Last update: Jan Swart, Dr. (14.02.2019)

Basic probability theory. Measure theory is a prerequisite, some prior experience with Markov chains is useful.

 
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