Stockholm-Uppsala Analysis and Probability Day 2015.

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

Date: Thursday, November 26, 2015.
Location: Polhemssalen, Ångströmlaboratoriet, Uppsala University.

  • Juhan Aru (ETH Zurich)
  • Mia Deijfen (Stockholm University)
  • Gaultier Lambert (KTH)
  • Seung-Yeop Lee (University of South Florida)
Organizers: Maurice Duits (KTH), Fredrik Viklund (KTH/Uppsala University). 

Schedule (Tentative)

13.00-14.00   Aru

Titles and Abstracts
  • Juhan Aru (ETH): 
    • TitleWhat would be a natural random measure on the sphere?
    • Abstract: I will discuss one possible answer that stems from the so called Liouville quantum gravity. I will try to explain why this is a natural answer, present two constructions that have been proposed in the literature and discuss why they are in fact equivalent. The very last part is joint work with Yichao Huang and Xin Sun.
  • Gaultier Lambert (KTH): 
    • TitleLinear statistics of determinantal point processes
    • AbstractI will present a method to compute the cumulants of linear statistics of determinantal point processes. Then, I will explain how it leads to Central Limits Theorems for statistics of unitary invariant Hermitian random matrices in various scalings. I will also provide an example motivated by the physic of free fermions where non-Gaussian fluctuations arise.  This is a joint work with Kurt Johansson. 
  • Mia Deijfen (Stockholm University): 
    • TitleThe speed and shape of first passage percolation on Z^2. 
    • AbstractFirst passage percolation on Z^2 is a model for the spread of an infection on the sites of the square lattice. The infection is spread via nearest neighbor sites and the time dynamic is specified by random passage times attached to the edges. We have studied the speed of the growth and the shape of the infected set by aid of large-scale computer simulations, with focus on continuous passage time distributions. I will report on our findings and speculate on implications for a version of the model with two competing infection types. 

      Joint work with Sven Erick Alm.

  • Seung-Yeop Lee (University of South Florida): 
    • TitleAsymptotics of characteristic polynomials in normal matrix ensemble
    • AbstractI will talk about the asymptotics of characteristic polynomials that appear in normal matrix ensemble.  I will derive the subleading behavior of the polynomials assuming the certain leading behavior.  The work is a joint work with Roman Riser.

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.