| 17-sep-2014 (wed) |
Clément Hongler
|
Ising model: making probabilistic sense of some conformal field theory ideas
|
17:15-18:15 |
HG G 43 |
| Abstract: |
Scaling limits of critical planar lattice models are conjectured to be described by Conformal Field Theory (CFT). The most classical example is the Ising model, which is expected to be described by a minimal model of CFT. We will discuss some progress in this direction: the proof of the conjectured formulae for the correlation functions using discrete complex analytic spinors and ways to make sense of the very objects and methods of CFT. Based on joined works with (mostly) Stéphane Benoist, Dmitry Chelkak, Konstantin Izyurov, Kalle Kytöla and Stanislav Smirnov. |
| Speakers: |
Clément Hongler
(EPF Lausanne)
|
|
| 1-oct-2014 (wed) |
Friedrich Götze
|
Spectral distribution of random matrices and free probability
|
17:15-18:15 |
HG G 43 |
| Abstract: |
We investigate the asymptotic spectral distribution of functions, in particular products, of classes of non-hermitian random matrices and discuss its relation to free Probability. Furthermore, we discuss two approaches to asymptotic expansions of Voiculescu's entropy for sums of free random variables. |
| Speakers: |
Friedrich Götze
(Universität Bielefeld)
|
|
| 8-oct-2014 (wed) |
Igor Kortchemski
|
Random stable looptrees and percolation on random planar maps
|
17:15-18:15 |
HG G 43 |
| Abstract: |
In this talk, we will introduce a class of random compact metric spaces L_alpha indexed by alpha in (1,2) and which we call looptrees. They are made of a collection of random loops glued together along a random tree structure, can informally be viewed as dual graphs of alpha-stable Lévy trees and are coded by a spectrally positive alpha-stable Lévy process. We will see that stable looptrees are universal scaling limits, for the Gromov-Hausdorff topology, of various combinatorial models. In particular, the stable looptree of parameter 3/2 is closely related to the scaling limits of cluster boundaries in critical site-percolation on large random triangulations. Based on joint works with Nicolas Curien. |
| Speakers: |
Igor Kortchemski
(Universität Zürich)
|
|
| 15-oct-2014 (wed) |
Vincent Tassion
|
Absence of percolation for critical Bernoulli percolation on planar slabs
|
17:15-18:15 |
HG G 43 |
| Abstract: |
We prove that the probability that there exists an infinite cluster for critical Bernoulli percolation
on Z2 times G for any finite graph G is equal to zero. This talk is based on a joint work with
H. Duminil-Copin and V. Sidoravicius. |
| Speakers: |
Vincent Tassion
(Université de Genève)
|
|
| 22-oct-2014 (wed) |
Nikolaos Zygouras
|
Scaling limits of disorder relevant and marginally relevant systems
|
17:15-18:15 |
HG G 43 |
| Abstract: |
We consider statistical mechanics models defined on a lattice, in which disorder acts as an external random field. Such models are called disorder relevant, if arbitrarily weak disorder changes the qualitative properties of the model. We show that, when the homogeneous model has a non-trivial continuum limit, disorder relevance manifests itself via the convergence of the disordered model to a disordered continuum limit, whose partition function is given in terms of a Wiener chaos expansion. Such are the cases of the 1+1 directed polymer (DPRM), the disorder pinning model with renewal exponent $\alpha >1/2$ and the 2d critical random field Ising model. Changing some parameters of the models, e.g. the dimension $d$ in the $1+d$ DPRM or the exponent $\alpha$ in the case of the pinning model may produce models, which are insensitive to disorder (disorder irrelevance). The point where this transition happens ($d=2$ for DPRM or $\alpha=1/2$ for pinning) is called marginal and it is the most subtle to analyse. In particular, the Wiener chaos expansion characterising the continuum limit of the corresponding disorder relevant model fails to make sense. However, a scaling limit, which is universal among the different marginally relevant models, still exists. Based on Joint work with F. Caravenna and R. Sun. |
| Speakers: |
Nikolaos Zygouras
(University of Warwick)
|
|
| 29-oct-2014 (wed) |
Patrik Ferrari
|
Free energy fluctuations for directed polymers in 1+1 dimension
|
17:15-18:15 |
HG G 43 |
| Abstract: |
The Kardar-Parisi-Zhang (KPZ) universality class includes directed polymers in random media in 1+1 dimension. According to the universality conjecture, for any finite temperature, the fluctuations of the free energy (e.g. for point-to-point) directed polymers is expected to be distributed as the (GUE) Tracy-Widom distribution in the limit of large system size. This distribution arose first in the context of random matrices. Detailed results as the fluctuation laws for models in the KPZ were, until recently, available only for "zero temperature models". We consider two models at positive temperature, a semi-discrete and the continuum directed polymer models, and determine the law of the free energy fluctuations. |
| Speakers: |
Patrik Ferrari
(Universität Bonn)
|
|
| 5-nov-2014 (wed) |
Jamal Najim
|
Large complex correlated Wishart matrices: Fluctuations and asymptotic independence at the edges
|
17:15-18:15 |
HG G 43 |
| Abstract: |
We study the asymptotic behavior of eigenvalues of large complex correlated Wishart matrices at the edges of the limiting spectrum. For this matrix model, the support of the limiting eigenvalue distribution may have several connected components. Under mild conditions, we will show that the extremal eigenvalue which converge almost surely towards the edges of the support fluctuate according to the Tracy-Widom law at the scale $N^2/3$. Moreover, given several generic positive edges, we establish that the associated extremal eigenvalue fluctuations are asymptotically independent. Finally, when the leftmost edge is the origin, we prove that the smallest eigenvalue fluctuates according to the hard-edge Tracy-Widom law at the scale $N^2$ (Bessel kernel). As an application, an asymptotic study of the condition number of large correlated Wishart matrices is provided. Joint work with Walid Hachem (Telecom Paristech and CNRS, France) and Adrien Hardy (KTH - Royal Institute of Technology, Sweden). |
| Speakers: |
Jamal Najim
(Université de Marne la Vallée)
|
|
| 12-nov-2014 (wed) |
Daisuke Shiraishi
|
Growth exponent for loop-erased random walk in three dimensions
|
15:15-16:15 |
HG G 19.2 |
| Abstract: |
Let S be the simple random walk on Z^d started at the origin. We think of its path up to time n, say S[0,n], as a random graph. Three objects we discuss are the loop erasure of S[0,n], the graph distance and the effective resistance between the origin and S(n) on S[0,n]. All of them are generated by the path S[0,n] and its asymptotic behavior depends on the dimension. In the talk, I will explain what's known (or unknown) and what I proved about them. |
| Speakers: |
Daisuke Shiraishi
(University of Kyoto)
|
|
| 26-nov-2014 (wed) |
|
Swiss Probability Seminar, Bern
|
13:00-18:00 |
Bern |
|
|
| 3-dec-2014 (wed) |
Christophe Garban
|
|
17:15-18:15 |
HG G 43 |
| Speakers: |
Christophe Garban
(ENS Lyon)
|
|
| 10-dec-2014 (wed) |
Jérémie Bettinelli
|
|
17:15-18:15 |
HG G 43 |
| Speakers: |
Jérémie Bettinelli
(Institut Elie Cartan, Nancy)
|
|
