Organized by: Dominique Bakry (Toulouse), Szymon Peszat (Cracow), and Bogusław Zegarliński (London).

The meeting will review recent results in the area of discrete and continuous probability/stochastics intertwined with related problems and methods of mathematical analysis. Besides a number of presentation by international participants, the meeting will include two 6 hrs mini-courses (suitable for PhD students and young researchers).

The venue is the Faculty of Applied Mathematics AGH University of Science and Technology, Al. Mickiewicza 30, connector A3-A4, room 304 for morning sessions and room 103 for afternoon sesions, see: the localization in the campus.

**Previous and related
activities:
**

- Workshop on Stochastic Analysis and Related Fields, Cracow 20 - 22 July, 2009
- Workshop on Analysis and Stochastic Analysis, Cracow 11 - 15 July, 2011
- CNRS-PAN Mathematics Summer Institute, Cracow 9 - 13 July, 2012
- Noncommutative Workshop, Cracow 9-12 September 2013

**Minicourses:**

- Charles Bordenave
(Toulouse): Spectrum of random graphs

**Abstract:**Following Benjamini/Schramm and Aldous/Lyons, we will introduce the unimodular and sofic graphs which are the natural limits of finite graph sequences with uniformly bounded degrees. For these graphs, we will define a proper notion of spectrum and study its properties. We will put the emphasis on the study of the regularity of the spectrum. Our main examples will be the spectral measure of supercritical percolation on the square grid and on the hypercube and of Erdos-Renyi graphs. If time allows, we will also discuss some connections with random matrices. - Djalil Chafaï
(Universite Paris-Est Marne-la-Vallee): Topics in random matrices
and potential theory

**
List of participants:**

- D. Bakry (Toulouse)
- C. Bordenave (Toulouse)
- W. Bednorz (Warsaw)

- R. Bogucki (Warsaw)

- D. Buraczewsk (Wrocław)
- K. Ciosmak (Warsaw)

- D. Chafaï (Paris)

- T. Chojecki (Lublin)

- I. Gentil (Lyon)

- B. Huou (Toulouse)

- A. Joulin (Toulouse)

- M. Kamińska (Warsaw)

- T. Komorowski (Warsaw/Lublin)
- R. Latała (Warsaw)

- C. Léonard (Paris)

- X. Liu (London)

- M. Majka (Cracow)

- E. Marciniak (Cracow)

- L. Miclo (Toulouse)

- P. Monmarché (Toulouse)

- P. Nayar (Warsaw)

- S. Peszat (Cracow)

- K. Pietruska-Pałuba (Warsaw)

- P. Przybyłowicz (Cracow)

- M. Strzelecki (Warsaw)

- T. Szarek (Gdańsk)

- T. Tkocz (Warwick)

- J. Trybuła (Cracow)

- M. Wasilewski (Warsaw)

- H. Wojewódka (Gdańsk)

- B. Zegarlinski (London)

- F. Zak (London)

For more information contact S. Peszat, e-mail napeszat[AT]cyf-kr.edu.pl

**Tentative Program: **

**Sunday 30 June Arrival day
**

**Monday 1 July**

- 10.00 - 10.40 A. Joulin: Intertwinings between Markov processes.
- 10.45 - 11.25 W. Bednorz: On the suprema of Bernoulli Processes.
- 11.30 - 12.00 D. Buraczewski: On solutions of linear stochastic equations in the critical case.
- 14.30 - 16.30 C. Bordenave: minicourse
- 16.30 - 16.50 T&C
- 16.50 - 17.35 C. Léonard: Dynamics of entropic interpolations.

**Tuesday 2 July**

- 10.00 - 10.45 K. Pietruska-Pałuba: Integrated density of states for Poisson perturbations of Markov processes on the Sierpinski gasket.
- 11.00 - 11.30 P. Monmarché: hypocoercive relaxation to equilibrium for kinetic models.
- 11.30 - 12.00 P. Nayar: Hopefully new L_1 Sobolev-type inequality.
- 15.00 - 17.00 C. Bordenave: minicourse
- 17.00 - 17.20 T&C
- 17.20 - 17.50 P. Przybyłowicz: Optimal approximation of scalar SDEs with time-irregular coefficients (asymptotic setting).
- 18.30 - 20.30 History of Science Evening, Aula Jagiellońska, Collegium Maius

**Wednesday 3 July**

- 9.30 - 11.30 D. Chafaï: minicourse
- 12.00 - 20.30 Excursion

**Thursday 4 July**

- 9.30 - 11.30 C. Bordenave: minicourse
- 11.30 - 11.50 T&C
- 11.50 - 12.30 H. Wojewódka: Exponential rate of convergence for some Markov operators.
- 15.00 - 17.00 D. Chafaï: minicourse
- 17.00 - 17.20 T&C
- 19.00 - Conference Dinner (Restaurant Nova, Estery 18)

**Friday 5 July**

- 9.30 - 11.30 D. Chafaï: minicourse
- 11.30 - 11.50 T&C
- 11.50 - 12.20 T. Tkocz: Tensor products of random unitary matrices.