CNRSIMPAN Mathematics Summer Institute, Cracow
2  9 July, 2017
In collaboration with the Institute of Mathematics, Jagiellonian
University, Institute of Mathematics, Polish Academy of Sciences,
CNRS, Imperial College London, IMP Universite Paul Sabatier Toulouse, and
ANR project STAB.
Supported by Warsaw Center of Mathematics and Computer Sciences.
Organizers: Dominique Bakry (Toulouse), Szymon Peszat (Cracow), and
Bogusław Zegarliński (London).
The meeting will review recent results in the area of
analysis/stochastics. Besides a number of presentation by international
participants, the meeting will include two minicourses (suitable
for PhD students and young researchers). It is probable that we will
be able to cover the accommodation of some number of participants (with
the strong emphasis of young people and researchers without financial
support of their organizations). In order to register, send an email to:
Szymon Peszat on e.mail adress napeszat@cyfkr.edu.pl
The venue of the workshop is: Room 0094, the main building of
the Faculty of Mathematics and Computer Sciences, Jagiellonian
University, Łojasiewicza 6, 30348 Kraków.
Previous and related activities:

CNRSPAN Mathematics Summer Institute, Cracow 27 June  2 July, 2016

CNRSPAN Mathematics Summer Institute, Cracow 28 June  4 July, 2015

CNRSPAN Mathematics Summer Institute, Cracow 26 June  4 July, 2014

CNRSPAN Mathematics Summer Institute, Cracow 1  7 July, 2013

Workshop on Analysis and Stochastic Analysis, Cracow 11  15 July,
2011

Workshop on Stochastic Analysis and Related Fields, Cracow 20  22 July,
2009

Noncommutative Workshop, Cracow 912 September 2013

Noncommutative Workshop, Cracow 2025 September 2015
Minicourses:
 Sergey Bobkov (Minneapolis): A second order concentration of measure on the sphere, and its application
to randomized central limit theorems.
Abstract: There will be discussed deviation inequalities for smooth
functions on the sphere with improved rates relying upon the second
partial derivatives (Hessians). Such results are illustrated in the problem
of rates of normal approximation for weighted sums of dependent
random variables under proper second order correlationtype conditions.

Persi Diaconis (Stanford): The mathematics of shuffling cards.
 Lecture 1 Introduction. These lectures will prove theorems about real
world methods of shuffling cards (e.g., it takes about 7 riffle shuffles
to mix up 52 cards). The first lecture sets up the problem and proves
the 7 shuffles theorem.
 Lecture 2 Adding numbers. When numbers are added in the usual way,
carries occur along the way. It turns out that the carries form a Markov
chain with an "amazing" transition matrix. Strange to say, these problems
are closely related to the mathematics of riffle shuffling.
 Lecture 3 Hyperplane walks. There is an elegant family of random walks
on the chambers of a hyperplane arrangement. This includes various
shuffling schemes. All these walks are explicitly diagonalizable and
have "closed form" stationary distributions.
 Lecture 4 shuffling cards and Hopf algebras. Hopf algebras are
algebraic "gadgets" used by topologists. In many examples,
the "Hopf square map" has a simple probabilistic interpretation.
The free associative algebra leads to riffle shuffles, symmetric functions
leads to a rock breaking model of Kolmogorov. The hard work done by
combinatorialists and others gives explicit forms of the eigenvectors.
 Lecture 5 Overhand shuffling. This commonly used method of mixing
needs different sets of tools for analysis, coupling, and comparison
theory will be introduced and do a pretty good job.
 Lecture 6 Smooshing. The "wash of smoosh" shuffle is widely used in
poker tournaments and in Monte Carlo. It involves sliding the cards
around on the table to mix them. I will introduce a fluid mechanics model
to study this and a novel coupling technique to get quantitative results.
Registered Participants: Dominique Bakry (Toulouse), Oliwier Biernacki
(Wrocław), Sergey Bobkov (Minneapolis), Dariusz Buraczewski (Wrocław),
Adam Burchardt (Poznań), Persi Diaconis (Stanford),
Jose Carillo (London), Jose A. Canizo (Granada), Klaudiusz Czudek (Gdańsk),
Gracjan Góral (Wrocław), Tomasz Kosmala (London),
Kajetan Jastrzębski (Wrocław), Zbigniew Jurek (Wrocław),
Xu Lihu (Macau),
Paweł Lorek (Wrocław), Piotr Markowski (Wrocław),
Laurent Miclo
(Toulouse), Wojtek Słomczyński (Cracow), Roman Srzednicki (Cracow), Miroslav Strupl (Prague), Tomasz Szarek (Gdańsk),
Maciej Szczeciński (Zielona Góra), Jacek Wesołowski (Warsaw),
Robert Wolstenholme (Prague), Filip Zagórski (Wrocław),
Frantisek Zak (Prague), Andrzej Zuk (Paris).
Talks:
Dariusz Buraczewski  Large deviations for random walks in random
environment.
Jose A. Canizo  Entropy production inequalities for the linear
Boltzmann equatiion.
Tomasz Kosmala  Variational solutions to SPDEs driven by cylindrical
Levy noise. Abstract: We prove the existence and uniqueness of solution
to an infinite dimensional evolution equation driven by a cylindrical Levy
process. It is assumed that the coefficients in the equation are monotone
and coercive. The solution is constructed as a limit of the Galerkin
approximation by projecting the equation onto ndimensional subspaces,
which enables us to use results from finite dimension.
Zbigniew Jurek  (Some) Ising models and the selfdecomposability property.
Abstract: Selfdecomposable distributions ( called also as the class L
distributions) appear as an extention of CLT. It is a quite big class that
includes stable measures, tStudent, Snedecor F, gamma, etc. We will show how
some of selfdecomposable distributions can be related to the Ising model for
ferromagnetism with the external (magnetisation) field.
Laurent Miclo  On Markov intertwinings. Abstract: After recalling the intertwining relation of the Brownian motion with the Bessel 3 process
due to Pitman (1975) and the use of a corresponding technique to deal with the convergence to equilibrium
for the toptorandom card shuffle by Aldous and Diaconis (1986), we will extend this procedure to
elliptic diffusions on manifolds via stochastic modifications of mean curvature flows.
Tomasz Szarek  Random function systems on the circle. Abstract: The
talk will be devoted to ergodicity of random function systems on the circle.
We show also that such systems, under very weak conditions, satisfy the law
of large numbers and central limit theorem.
Lihu Xu  Convergence rate of stable law. Abstract: By Stein's method,
we prove a general inequality of stable law. As an application, we give the
convergence rate for an example which appears in many textbooks.
Andrzej Zuk  Random walks on ultra discrete limits.
Program:
Sunday 2 July
Arrival Day
Monday 3 July
10.00  10.30 T&C
10.30  12.00 Persi Diaconis (Minicourse 1)
Lunch
13.30  15.00 Sergey Bobkov (Minicourse 1)
15.00  15.30 T&C
15.30  16.15 Jose A. Canizo (Entropy production inequalities for the linear
Boltzmann equatiion)
16.20  16.50 Tomasz Kosmala (Variational solutions to SPDEs
driven by cylindrical Levy noise)
Tuesday 4 July
10.00  10.30 T&C
10.30  12.00 Sergey Bobkov (Minicourse 2)
Lunch
13.30  15.00 Persi Diaconis (Minicourse 2)
15.00  15.30 T&C
15.30  16.15 Laurent Miclo (On Markov intertwinings)
16.20  17.05 Zbigniew Jurek ((Some) Ising models and the selfdecomposability
property)
Wednesday 5 July
10.00  10.30 T&C
10.30  12.00 Sergey Bobkov (Minicourse 3)
Thursday 6 July
10.00  10.30 T&C
10.30  12.00 Persi Diaconis (Minicourse 3)
Lunch
13.30  14.15 Tomasz Szarek (Random function systems on the circle)
14.15  14.30 T&C
14.30  15.15 Lihu Xu (Convergence rate of stable law)
15.30  16.15 Dariusz Buraczewski (Large deviations for random walks
in random environment)
Friday 7 July
10.00  10.30 T&C
10.30  12.00 Persi Diaconis (Minicourse 4)
Lunch
13.30  14.15 Andrzej Zuk (Random walks on ultra discrete limits)
14.15  14.30 T&C