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BROWNIAN MOTION AND STOCHASTIC CALCULUS

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Master class in planar statistical physic 2015-2016
Chelkak Dmitry
Thursday 24 September 2015
Faculté des sciences - Section de mathématiques
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Collection

NCCR SwissMAP – Master Class in Planar Statistical Physics

1
INTRODUCTION TO STATISTICAL MECHANICS

INTRODUCTION TO STATISTICAL MECHANICS

Yvan Velenik
Tuesday 15 September 2015
2
BROWNIAN MOTION AND STOCHASTIC CALCULUS

BROWNIAN MOTION AND STOCHASTIC CALCULUS

Dmitry Chelkak
Thursday 17 September 2015
3
GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

Hugo Duminil
Friday 18 September 2015
4
MARTINGALES AND MARKOV PROCESSES (1/2)

MARTINGALES AND MARKOV PROCESSES (1/2)

Wu Hao
Monday 21 September 2015
5
MARTINGALES AND MARKOV PROCESSES (2/2)

MARTINGALES AND MARKOV PROCESSES (2/2)

Wu Hao
Monday 21 September 2015
6
INTRODUCTION TO STATISTICAL MECHANICS

INTRODUCTION TO STATISTICAL MECHANICS

Yvan Velenik
Tuesday 22 September 2015
7
BROWNIAN MOTION AND STOCHASTIC CALCULUS

BROWNIAN MOTION AND STOCHASTIC CALCULUS

Dmitry Chelkak
Thursday 24 September 2015
8
GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

Hugo Duminil
Friday 25 September 2015
9
MARTINGALES AND MARKOV PROCESSES (1/2)

MARTINGALES AND MARKOV PROCESSES (1/2)

Wu Hao
Monday 28 September 2015
10
MARTINGALES AND MARKOV PROCESSES (2/2)

MARTINGALES AND MARKOV PROCESSES (2/2)

Wu Hao
Monday 28 September 2015
11
INTRODUCTION TO STATISTICAL MECHANICS

INTRODUCTION TO STATISTICAL MECHANICS

Yvan Velenik
Tuesday 29 September 2015
12
BROWNIAN MOTION AND STOCHASTIC CALCULUS

BROWNIAN MOTION AND STOCHASTIC CALCULUS

Dmitry Chelkak
Thursday 1 October 2015
13
GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

Hugo Duminil
Friday 2 October 2015
14
MARTINGALES AND MARKOV PROCESSES

MARTINGALES AND MARKOV PROCESSES

Wu Hao
Monday 5 October 2015
15
INTRODUCTION TO STATISTICAL MECHANICS

INTRODUCTION TO STATISTICAL MECHANICS

Yvan Velenik
Tuesday 6 October 2015
16
BROWNIAN MOTION AND STOCHASTIC CALCULUS

BROWNIAN MOTION AND STOCHASTIC CALCULUS

Dmitry Chelkak
Thursday 8 October 2015
17
GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

Hugo Duminil
Friday 9 October 2015
18
MARTINGALES AND MARKOV PROCESSES

MARTINGALES AND MARKOV PROCESSES

Wu Hao
Monday 12 October 2015
19
INTRODUCTION TO STATISTICAL MECHANICS

INTRODUCTION TO STATISTICAL MECHANICS

Yvan Velenik
Tuesday 13 October 2015
20
BROWNIAN MOTION AND STOCHASTIC CALCULUS 1/2

BROWNIAN MOTION AND STOCHASTIC CALCULUS 1/2

Dmitry Chelkak
Thursday 15 October 2015
21
BROWNIAN MOTION AND STOCHASTIC CALCULUS 2/2

BROWNIAN MOTION AND STOCHASTIC CALCULUS 2/2

Dmitry Chelkak
Thursday 15 October 2015
22
GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

Hugo Duminil
Friday 16 October 2015
23
MARTINGALES AND MARKOV PROCESSES

MARTINGALES AND MARKOV PROCESSES

Wu Hao
Monday 19 October 2015
24
INTRODUCTION TO STATISTICAL MECHANICS

INTRODUCTION TO STATISTICAL MECHANICS

Yvan Velenik
Tuesday 20 October 2015
25
GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

Hugo Duminil
Friday 23 October 2015
26
MARTINGALES AND MARKOV PROCESSES (1/2)

MARTINGALES AND MARKOV PROCESSES (1/2)

Wu Hao
Monday 26 October 2015
27
MARTINGALES AND MARKOV PROCESSES (2/2)

MARTINGALES AND MARKOV PROCESSES (2/2)

Wu Hao
Monday 26 October 2015
28
INTRODUCTION TO STATISTICAL MECHANICS

INTRODUCTION TO STATISTICAL MECHANICS

Yvan Velenik
Tuesday 27 October 2015
29
BROWNIAN MOTION AND STOCHASTIC CALCULUS

BROWNIAN MOTION AND STOCHASTIC CALCULUS

Dmitry Chelkak
Thursday 29 October 2015
30
GEOMETRIC REPRESENTATIONS OF LATTICE MODELS (1/2)

GEOMETRIC REPRESENTATIONS OF LATTICE MODELS (1/2)

Matan Harel
Friday 30 October 2015
31
GEOMETRIC REPRESENTATIONS OF LATTICE MODELS (2/2)

GEOMETRIC REPRESENTATIONS OF LATTICE MODELS (2/2)

Matan Harel
Friday 30 October 2015
32
MARTINGALES AND MARKOV PROCESSES

MARTINGALES AND MARKOV PROCESSES

Wu Hao
Monday 2 November 2015
33
INTRODUCTION TO STATISTICAL MECHANICS

INTRODUCTION TO STATISTICAL MECHANICS

Yvan Velenik
Tuesday 3 November 2015
34
BROWNIAN MOTION AND STOCHASTIC CALCULUS

BROWNIAN MOTION AND STOCHASTIC CALCULUS

Dmitry Chelkak
Thursday 5 November 2015
35
GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

Matan Harel
Friday 6 November 2015
36
MARTINGALES AND MARKOV PROCESSES

MARTINGALES AND MARKOV PROCESSES

Wu Hao
Monday 9 November 2015
37
INTRODUCTION TO STATISTICAL MECHANICS

INTRODUCTION TO STATISTICAL MECHANICS

Yvan Velenik
Tuesday 10 November 2015
38
Brownian Motion and Stochastic Calculus

Brownian Motion and Stochastic Calculus

Dmitry Chelkak
Thursday 12 November 2015
39
Geometric Representations of Lattice Models

Geometric Representations of Lattice Models

Hugo Duminil
Friday 13 November 2015
40
GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

Hugo Duminil
Tuesday 17 November 2015
41
BROWNIAN MOTION AND STOCHASTIC CALCULUS (1/2)

BROWNIAN MOTION AND STOCHASTIC CALCULUS (1/2)

Dmitry Chelkak
Thursday 19 November 2015
42
BROWNIAN MOTION AND STOCHASTIC CALCULUS (2/2)

BROWNIAN MOTION AND STOCHASTIC CALCULUS (2/2)

Dmitry Chelkak
Thursday 19 November 2015
43
INTRODUCTION TO STATISTICAL MECHANICS

INTRODUCTION TO STATISTICAL MECHANICS

Yvan Velenik
Friday 20 November 2015
44
MARTINGALES AND MARKOV PROCESSES 1/2

MARTINGALES AND MARKOV PROCESSES 1/2

Wu Hao
Monday 23 November 2015
45
MARTINGALES AND MARKOV PROCESSES 2/2

MARTINGALES AND MARKOV PROCESSES 2/2

Wu Hao
Monday 23 November 2015
46
INTRODUCTION TO STATISTICAL MECHANICS 1/2

INTRODUCTION TO STATISTICAL MECHANICS 1/2

Yvan Velenik
Tuesday 24 November 2015
47
INTRODUCTION TO STATISTICAL MECHANICS 2/2

INTRODUCTION TO STATISTICAL MECHANICS 2/2

Yvan Velenik
Tuesday 24 November 2015
48
BROWNIAN MOTION AND STOCHASTIC CALCULUS

BROWNIAN MOTION AND STOCHASTIC CALCULUS

Dmitry Chelkak
Thursday 26 November 2015
49
GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

Hugo Duminil
Friday 27 November 2015
50
MARTINGALES AND MARKOV PROCESSES

MARTINGALES AND MARKOV PROCESSES

Wu Hao
Monday 30 November 2015
51
INTRODUCTION TO STATISTICAL MECHANICS

INTRODUCTION TO STATISTICAL MECHANICS

Yvan Velenik
Tuesday 1 December 2015
52
BROWNIAN MOTION AND STOCHASTIC CALCULUS

BROWNIAN MOTION AND STOCHASTIC CALCULUS

Dmitry Chelkak
Thursday 3 December 2015
53
GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

Hugo Duminil
Friday 4 December 2015
54
INTRODUCTION TO STATISTICAL MECHANICS

INTRODUCTION TO STATISTICAL MECHANICS

Yvan Velenik
Tuesday 8 December 2015
55
BROWNIAN MOTION AND STOCHASTIC CALCULUS

BROWNIAN MOTION AND STOCHASTIC CALCULUS

Dmitry Chelkak
Thursday 10 December 2015
56
GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

GEOMETRIC REPRESENTATIONS OF LATTICE MODELS

Hugo Duminil
Friday 11 December 2015
57
MARTINGALES AND MARKOV PROCESSES

MARTINGALES AND MARKOV PROCESSES

Wu Hao
Monday 14 December 2015
58
BROWNIAN MOTION AND STOCHASTIC CALCULUS 1/2

BROWNIAN MOTION AND STOCHASTIC CALCULUS 1/2

Dmitry Chelkak
Thursday 17 December 2015
59
BROWNIAN MOTION AND STOCHASTIC CALCULUS 2/2

BROWNIAN MOTION AND STOCHASTIC CALCULUS 2/2

Dmitry Chelkak
Thursday 17 December 2015
60
ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

David Cimasoni
Tuesday 23 February 2016
61
Conformal invariance of lattice models

Conformal invariance of lattice models

Stanislav Smirnov
Friday 26 February 2016
62
Conformal Invariance Of Lattice Models

Conformal Invariance Of Lattice Models

Stanislav Smirnov
Monday 29 February 2016
63
ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

David Cimasoni
Tuesday 1 March 2016
64
CONFORMAL INVARIANCE OF LATTICE MODELS

CONFORMAL INVARIANCE OF LATTICE MODELS

Stanislav Smirnov
Friday 4 March 2016
65
ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

David Cimasoni
Tuesday 8 March 2016
66
CONFORMAL INVARIANCE OF LATTICE MODELS

CONFORMAL INVARIANCE OF LATTICE MODELS

Stanislav Smirnov
Monday 14 March 2016
67
ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

David Cimasoni
Tuesday 15 March 2016
68
CONFORMAL INVARIANCE OF LATTICE MODELS

CONFORMAL INVARIANCE OF LATTICE MODELS

Stanislav Smirnov
Friday 18 March 2016
69
CONFORMAL INVARIANCE OF LATTICE MODELS

CONFORMAL INVARIANCE OF LATTICE MODELS

Stanislav Smirnov
Monday 21 March 2016
70
ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

David Cimasoni
Tuesday 22 March 2016
71
ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

David Cimasoni
Tuesday 5 April 2016
72
PEELING OF RANDOM PLANAR MAPS (1/2)

PEELING OF RANDOM PLANAR MAPS (1/2)

Curien Nicolas
Tuesday 5 April 2016
73
PEELING OF RANDOM PLANAR MAPS (2/2)

PEELING OF RANDOM PLANAR MAPS (2/2)

Curien Nicolas
Tuesday 5 April 2016
74
ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

David Cimasoni
Tuesday 12 April 2016
75
PEELING OF RANDOM PLANAR MAPS (1/2)

PEELING OF RANDOM PLANAR MAPS (1/2)

Curien Nicolas
Tuesday 12 April 2016
76
PEELING OF RANDOM PLANAR MAPS (2/2)

PEELING OF RANDOM PLANAR MAPS (2/2)

Curien Nicolas
Tuesday 12 April 2016
77
Conformal Invariance Of Lattice Models (1/2)

Conformal Invariance Of Lattice Models (1/2)

Stanislav Smirnov
Friday 15 April 2016
78
Conformal Invariance Of Lattice Models (2/2)

Conformal Invariance Of Lattice Models (2/2)

Stanislav Smirnov
Friday 15 April 2016
79
Conformal Invariance Of Lattice Models

Conformal Invariance Of Lattice Models

Stanislav Smirnov
Monday 18 April 2016
80
ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

David Cimasoni
Tuesday 19 April 2016
81
PEELING OF RANDOM PLANAR MAPS (1/2)

PEELING OF RANDOM PLANAR MAPS (1/2)

Curien Nicolas
Tuesday 19 April 2016
82
PEELING OF RANDOM PLANAR MAPS (2/2)

PEELING OF RANDOM PLANAR MAPS (2/2)

Curien Nicolas
Tuesday 19 April 2016
83
ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

David Cimasoni
Tuesday 26 April 2016
84
PEELING OF RANDOM PLANAR MAPS (1/2)

PEELING OF RANDOM PLANAR MAPS (1/2)

Curien Nicolas
Tuesday 26 April 2016
85
PEELING OF RANDOM PLANAR MAPS (2/2)

PEELING OF RANDOM PLANAR MAPS (2/2)

Curien Nicolas
Tuesday 26 April 2016
86
Random Trees

Random Trees

Jean-François Le Gall
Friday 29 April 2016
87
ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

David Cimasoni
Tuesday 3 May 2016
88
RANDOM PLANAR MAPS

RANDOM PLANAR MAPS

Jean-François Le Gall
Tuesday 3 May 2016
89
CONFORMAL INVARIANCE OF LATTICE MODELS

CONFORMAL INVARIANCE OF LATTICE MODELS

Stanislav Smirnov
Friday 6 May 2016
90
ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

David Cimasoni
Tuesday 10 May 2016
91
RANDOM PLANAR MAPS

RANDOM PLANAR MAPS

Jean-François Le Gall
Tuesday 10 May 2016
92
CONFORMAL INVARIANCE OF LATTICE MODELS

CONFORMAL INVARIANCE OF LATTICE MODELS

Stanislav Smirnov
Friday 13 May 2016
93
ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

David Cimasoni
Tuesday 17 May 2016
94
RANDOM PLANAR MAPS

RANDOM PLANAR MAPS

Jean-François Le Gall
Tuesday 17 May 2016
95
CONFORMAL INVARIANCE OF LATTICE MODELS

CONFORMAL INVARIANCE OF LATTICE MODELS

Stanislav Smirnov
Saturday 21 May 2016
96
ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

David Cimasoni
Tuesday 24 May 2016
97
Conformal Invariance Of Lattice Models

Conformal Invariance Of Lattice Models

Stanislav Smirnov
Friday 27 May 2016
98
ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

ON VARIOUS ASPECTS OF THE DIMER AND ISING MODELS

David Cimasoni
Tuesday 31 May 2016