Stockholm-Uppsala Analysis and Probability Day 2014.

A one-day meeting focussing on recent developments at the intersection of analysis and probability.

Date: Friday, September 19, 2014.
Location: Department of Mathematics, Kräftriket House 5, Stockholm University, Room 14. Instructions for how to get there.

Confirmed speakers

Organizers: Maurice Duits (Stockholm University), Fredrik Viklund (Uppsala University/KTH). 

Registration is required but free.

Schedule

 Time             
9.30-10.30     Virag
10.30-11.00Coffee
11.00-12.00Hongler 
12.00-12.30Lis
12.30-14.00Lunch at Kräftan
14.00-15.00Knowles
15.00-15.30    Duse
15.30-16.00Coffee
16.00-17.00O'Connell 
17.00-            Wine and cheese     


Titles and Abstracts
  • Balint Virag (University of Toronto): 
    • TitleMean quantum percolation
    • Abstract: It is an open problem whether the limiting eigenvalue distribution of supercritical percolation in a large box has an absolutely continuous part. In joint work with Charles Bordenve and Arnab Sen we can show that non-atomic part exists in many models, including sparse Erdos-Renyi graphs. I will review the background and some new methods.
  • Clement Hongler (EPFL Lausanne):
    • Title:  Ising Model: making probabilistic sense of some Conformal Field Theory ideas
    • 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.

    • Marcin Lis (Chalmers/VU)
      • Title: The critical point of the Ising model via the Kac-Ward formula
      • Abstract: I will present a fairly elementary computation of the critical point of the Ising model on the square lattice using the Kac-Ward formula for the partition function. The method generalizes to the setup of aperiodic isoradial graphs yielding criticality of the so-called self-dual Z-invariant coupling constants. This is partially joint work with Wouter Kager and Ronald Meester.
    • Antti Knowles (ETH Zurich): 
      • TitleAnisotropic local laws for random matrices
      • Abstract:  Most of the literature on random matrices focuses on matrix models that are isotropic in the sense that their Green functions are close to a multiple of the identity matrix. Such models include Wigner matrices, Erdos-Renyi graphs, and random band matrices. I will talk about matrix models that are not isotropic. An important family of examples is provided by sample covariance matrices whose underlying population has nontrivial correlations. I present a new method that yields local laws for such anisotropic models. Applications include spectral universality, a complete analysis of outliers, and the identification of the (nonuniversal) eigenvector distribution. This is based on joint work with Jun Yin.
    • Erik Duse (KTH)
      • Title: Asymptotic geometry of phase diagrams of Gelfand-Testlin patterns on Z.
      • Abstract: Using methods of complex and harmonic analysis one can recover the asymptotic geometry of phase diagrams of the set Gelfand-Testlin patterns on Z with uniform probability and a fixed start configuration. An equivalent formulation in terms of backwards uniform Markov  dynamics on partitions will also be given.

    • Neil O'Connell (Warwick)
      • Title: Geometric RSK correspondence, Whittaker functions and random polymers
      • Abstract: The Robinson-Schensted-Knuth (RSK) correspondence is a combinatorial bijection which plays an important role in the theory of Young tableaux and provides a natural framework for the study of last passage percolation and longest increasing subsequence problems.  In this talk I will explain how a `geometric' (or `de-tropicalized')  version of the RSK mapping provides a similar framework for the study of Whittaker  functions and random polymers, mainly based on recent joint works with Ivan Corwin, Timo Seppalainen and Nikos Zygouras.

    About the meeting
    The interplay between analysis and probability has a long history and a strong tradition in the Stockholm-Uppsala area. Developments in these directions have in recent years accelerated, and probabilistic techniques and view-points are now essential parts of several of today's most exciting and active fields which often have close connections with mathematical physics.

    The Stockholm-Uppsala Analysis and Probability Day is an annual one-day meeting (held for the first time in the fall of 2014) focussing on the interplay between analysis, probability, and mathematical physics. The purpose is not only to promote problems and new ideas at the intersection of these fields, but also to strengthen the ties between the mathematics departments and relevant groups in Uppsala and Stockholm. The meeting is made possible thanks to funding from the mathematics departments of Stockholm University and Uppsala University.