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1 = Introduction to mathematical physics, spring 2011 =
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3 = (% style="color: rgb(51,51,51);" %)**Stochastic particle systems**(%%) =
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5 === Lecturer ===
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7 [[Antti Kupiainen>>doc:mathstatHenkilokunta.Kupiainen, Antti]]
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9 === Scope ===
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11 10 cu.
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13 === Type ===
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15 Advanced studies
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17 === (% style="color: rgb(51,51,51);" %)**Description**(%%) ===
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19 Stochastic particle systems (or "Interacting particle systems") are stochastic processes that are widely
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21 used in physics (in non-equilibrium statistical mechanics) and in biology (spatial population dynamics).
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23 In the simplest case (the simple exclusion process) particles perform random jumps on a lattice with
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25 the constraint that no site contains more than one particle. The course provides an introduction to the
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27 mathematical theory of these processes and then discusses in more detail the simple exclusion process
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29 where recently some remarkable connections to combinatorics and random matrices have been obtained.
30
31 === (% style="color: rgb(51,51,51);" %)**Contents**(%%) ===
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33 Review of probability
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35 Markov jump processes and their generators
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37 Particle systems: simple exclusion process (SEP), zero range process
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39 Hydrodynamic limit
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41 One dimensional SEP: random matrices, KPZ equation, universality
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43 === Prerequisites ===
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45 Basic probabiity
46
47 === (% style="color: rgb(51,51,51);" %)**Lectures**(%%) ===
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49 Weeks 4-9 and 11-18 tuesday 14-16, thursday 14-16 C123.
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51 Easter holiday 21.-27.4.
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53 === (% style="color: rgb(51,51,51);" %)**First lecture: Thursday January 27!!**(%%) ===
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55 === (% style="color: rgb(51,51,51);" %)**No lectures on Tuesday April 5 and Thursday April 7!!**(%%) ===
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57 === (% style="color: rgb(51,51,51);" %)**Next lecture: Thursday April 28!!**(%%) ===
58
59 === Lecture notes ===
60
61 [[Pages 1-59>>attach:Luennot1-59.pdf]]
62 [[Pages 60-78>>attach:Luennot60-78.pdf]]
63 [[Pages 79-89>>attach:Luennot79-89.pdf]]
64 [[Pages 90-98>>attach:Luennot90-98.pdf]]
65 [[Pages 100-127>>attach:Luennot100-127.pdf]]
66
67 === Exams ===
68
69 The exam is on thursday the 11th of August at 10-14.
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71 === Bibliography ===
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73 Timo Seppäläinen: Translation Invariant Exclusion Processes [[http:~~/~~/www.math.wisc.edu/~~~~seppalai/excl-book/ajo.pdf>>url:http://www.math.wisc.edu/~~seppalai/excl-book/ajo.pdf||shape="rect"]]
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75 T. M. Liggett: Interacting particle systems, volume 276 of Grundlehren der Mathematischen Wissenschaften, Springer- Verlag, New York, 1985
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77 H. Spohn. Large scale dynamics of interacting particles. Springer-Verlag, Berlin, 1991
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79 === [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=57357||shape="rect"]] ===
80
81 Did you forget to register? [[What to do>>doc:mathstatOpiskelu.Kysymys4]].
82
83 === Exercise groups ===
84
85 |=(((
86 Group
87 )))|=(((
88 Day
89 )))|=(((
90 Time
91 )))|=(((
92 Place
93 )))|=(((
94 Instructor
95 )))
96 |(((
97 1.
98 )))|(((
99 Fri
100 )))|(((
101 14-16
102 )))|(((
103 C122
104 )))|(((
105 Christian Webb
106 )))
107
108 === Exercises ===
109
110 ===== Due to Ferrari's course, the first exercise session will be on (% style="text-decoration: underline;" %)THURSDAY(%%) the 10th at 12.15 in the classroom (% style="text-decoration: underline;" %)B120(%%). =====
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112 [[Exercise 1>>attach:ex1.pdf]] [[Solutions 1>>attach:solutions1.pdf]]
113 [[Exercise 2>>attach:ex2.pdf]] [[Solutions 2>>attach:solutions2.pdf]]
114 [[Exercise 3>>attach:ex3.pdf]] [[Solutions 3>>attach:solutions3.pdf]]
115 [[Exercise 4>>attach:ex4.pdf]] [[Solutions 4>>attach:solutions4.pdf]]
116 [[Exercise 5>>attach:ex5.pdf]] [[Solutions 5>>attach:solutions5.pdf]]
117 [[Exercise 6>>attach:ex6.pdf]] [[Solutions 6>>attach:solutions6.pdf]]
118 [[Exercise 7>>attach:ex7.pdf]]
119 [[Exercise 8>>attach:ex8.pdf]]
120 [[Exercise 9>>attach:ex9.pdf]]