| 22-feb-2012 (wed) |
Martin Hairer
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Solving the KPZ equation
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17:15-18:15 |
HG G 43 |
| Abstract: |
The solution to the KPZ equation is believed to be a ``universal'' object describing the crossover between the Gaussian universality class and the KPZ universality class. The mathematical proof of its universality however is still an open problem, in particular because of the lack of a good approximation theory for the equation.
We will present a new notion of solution to the KPZ equation that bypasses the use of the Cole-Hopf transform. It allows to factorise the solution map into a ``universal'' (independent of initial condition) measurable map, composed with a solution map with good continuity properties. This lays the foundations for a robust approximation theory to the KPZ equation, which is needed to prove its universality. As a byproduct of the construction, we obtain very detailed regularity estimates on the solutions, as well as new homogenisation results. |
| Speakers: |
Martin Hairer
(University of Warwick, UK)
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| 29-feb-2012 (wed) |
Gaëtan Borot
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All order finite size corrections in Coulomb gases
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17:15-18:15 |
HG G 43 |
| Abstract: |
A Coulomb gas, also named $beta$ ensemble in random matrix theory, consists in N charged particules on the real line, trapped in a potential and interacting mutually by logarithmic repulsion, with inverse temperature $beta$. When N is large, heuristic arguments suggest that the partition function and the n-point correlation functions have a 1/N expansion when the particles condensate on one segment (one-cut regime), whereas oscillatory terms in N appears when they condensate on several disconnected segments. I will present a result stating the existence of the 1/N expansion for any fixed beta, under appropriate assumptions corresponding to the one-cut regime. The coefficients can be effectively computed to all orders. As an application, I will describe predictions of the all-order asymptotic tails of Tracy-Widom beta laws. This talk is based on joint works with A. Guionnet, and B. Eynard, S.N. Majumdar and C. Nadal. |
| Speakers: |
Gaëtan Borot
(Université de Genève)
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| 1-mar-2012 (thu) |
Ross Pinsky
|
Probabilistic and combinatorial aspects of the card-cyclic to random insertion shuffle
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15:15-17:00 |
tba |
| Abstract: |
Consider a permutation $\sigma\in S_n$ as a deck of cards numbered from 1 to $n$ and laid out in a row, where $\sigma_j$ denotes the number of the card that is in the $j$-th position from the left.\rm\ We study some probabilistic and combinatorial aspects of the shuffle on $S_n$ defined by removing and then randomly reinserting each of the $n$ cards once, with the removal and reinsertion being performed according to the original left to right order of the cards. The novelty here in this nonstandard shuffle is that every card is removed and reinserted exactly once. The bias that remains turns out to be quite strong and possesses some surprising features. |
| Speakers: |
Ross Pinsky
(Technion Haifa)
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| 7-mar-2012 (wed) |
Rajat Subhra Hazra
|
Patterned Random Matrices
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17:15-18:15 |
HG G 43 |
| Abstract: |
In this talk we focus on some recent results on large symmetric random matrices like Wigner, Toeplitz, Hankel, Circulant, Reverse Circulant etc. We show that they have some structural pattern which allows the limiting spectral distribution to exist. We also show that the joint convergence of different kinds of random matrices in the limit give rise to different notions of independence on non-commutative probability spaces. We point out some results and conjectures on the edge behavior of these matrices. |
| Speakers: |
Rajat Subhra Hazra
(Universität Zürich)
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| 14-mar-2012 (wed) |
Antti Knowles
|
Universality and non-universality in deformed random matrix ensembles
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17:15-18:15 |
HG G 43 |
| Abstract: |
Large random matrices exhibit the striking phenomenon of universality: under very general assumptions on the matrix entries, the limiting spectral statistics coincide with those of a Gaussian matrix ensemble. In the first part of the talk, I review recent results on the spectral universality of random matrices. The second part of the talk is devoted to deformed random matrix models, which exhibit an intriguing phase transition associated with the creation or annihilation of outlier eigenvalues. (Joint work with Jun Yin.) |
| Speakers: |
Antti Knowles
(Harvard University )
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| 21-mar-2012 (wed) |
Adela Svejda
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|
17:15-18:15 |
HG G 43 |
| Speakers: |
Adela Svejda
(Universität Bonn)
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| 28-mar-2012 (wed) |
Peter Pfaffelhuber
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|
17:15-18:15 |
HG G 43 |
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| 4-apr-2012 (wed) |
Adam Harper
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|
17:15-18:15 |
HG G 43 |
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| 11-apr-2012 (wed) |
Djalil Chafaï
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|
17:15-18:15 |
HG G 43 |
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| 18-apr-2012 (wed) |
Rob van den Berg
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|
17:15-18:15 |
HG G 43 |
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| 25-apr-2012 (wed) |
Sylvie Méléard
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|
17:15-18:15 |
HG G 43 |
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| 2-may-2012 (wed) |
Christina Goldschmidt
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|
17:15-18:15 |
HG G 43 |
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| 9-may-2012 (wed) |
|
Swiss Probability Seminar
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14:00-18:00 |
Universität Bern, Sidlerstrasse 5, A6 |
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| 16-may-2012 (wed) |
Nicolas Curien
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|
17:15-18:15 |
HG G 43 |
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| 23-may-2012 (wed) |
Joaquin Fontbona
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|
17:15-18:15 |
HG G 43 |
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| 30-may-2012 (wed) |
Jean-Christophe Mourrat
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|
17:15-18:15 |
HG G 43 |
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| 6-jun-2012 (wed) |
Mike Cranston
|
|
17:15-18:15 |
HG G 43 |
| Speakers: |
Mike Cranston
(University of Irvine)
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