Stochastic Sauna
Aalto University, December 19–20, 2024
Stochastic Sauna is a traditional workshop that brings together researchers and students working on probability, statistics, and their applications. The workshop will be held on Thu 19–Fri 20 December 2024.
Confirmed speakers
 Dirk Blömker (University of Augsburg)
 Ariane Carrance (University of Vienna)
 Colin Desmarais (TU Wien)
 Mohamed Fkirine (Tampere University)
 Alex Karrila (Åbo Akademi University)
 Petri Laarne (University of Helsinki)
 Mikko Parviainen (University of Jyväskylä)
 István Prause (Åbo Akademi University)
 Lukas Schoug (University of Helsinki)
 Paul Thevenin (Angers University)
 Xilin Zhou (University of Jyväskylä)
Venue
All talks take place at Hall M1, Aalto University, Otakaari 1, Espoo, Finland. The lecture hall is equipped with a blackboard, beamer, and a computer.
Tentative Schedule



9:50 
Opening 

10:00–10:45 


11:00–11:45 


12–13 
Lunch (selforganized) 

13:00–13:45 


14:00–14:45 


14:45–15:15 
Coffee 

15:15–16:00 


17:00–19:00 
Social program (Sauna @ Löyly, Hernesaarenranta 4, Helsinki) 

20:00 
Dinner (selforganized @ Zetor, Mannerheimintie 3–5, Helsinki) 




Fri, Dec 20, 2024 





10:00–10:45 


11:00–11:45 


12–13 
Lunch (selforganized) 

13:00–13:45 


14:00–14:45 


14:45–15:15 
Coffee 

15:15–16:00 


16:15–17:00 


Social program
The social program includes sauna (@ Löyly, Hernesaarenranta 4, Helsinki). Sauna is free for participants. Sauna is mixed, but the changing rooms will be reserved for male and female participants. Please bring your bathing suit. We have reserved tables at Restaurant Zetor, Mannerheimintie 3–5, Helsinki for the social dinner.
Registration
There is no participation fee, but registration is mandatory. Please fill in the registration form.
Abstracts
Dirk Blömker (University of Augsburg)
Ariane Carrance (University of Vienna)
Colin Desmarais (TU Wien)
Mohamed Fkirine (Tampere University)
Alex Karrila (Åbo Akademi University)
Uniform spanning trees, degenerate correlation functions of CFT, and fused SLEs
The uniform random spanning tree (UST) on a finite subgraph of the integer lattice Z^2 is an archetypal example of a critical discrete planar model, which are generally expected to exhibit conformal invariance in the scaling limit. Many such properties have also been proven over the past two decades, e.g., in terms of physics predictions from Conformal field theory (CFT), or purely mathematically in terms of conformally invariant random geometry.
In the present talk, we study connectivity events of multiple UST boundary branches, with potentially fused endpoints and in any topological connectivity. The scaling limits of their probabilities are found explicitly and shown to satisfy various properties of CFT (c=2) degenerate correlation functions, in particular conformal covariance, fusion rules, and socalled BPZ PDEs. In CFT language, these limits are interpreted as covering the entire first row of the Kac table, hence providing arguably the widest rigorously known dictionary between a discrete model and a CFT. In the random geometry direction, we rigorously relate both the discrete model and the limiting probabilities to fused SLE (kappa=2) type random curves.
Based on an ongoing work with Augustin Lafay, Eveliina Peltola and Julien Roussillon.
Petri Laarne (University of Helsinki)
Metastable dynamics of the hyperbolic phi^4 model
We consider a stochastic wave equation with a symmetric doublewell potential. The solutions spend long times near potential minima, but jump occasionally between them. What is the average frequency of jumping? I will sketch how this is answered with stochastic quantization. I will also briefly comment on the very different parabolic problem.
Based on recent preprint (arXiv:2410.03495) with Nikolay Barashkov.
Mikko Parviainen (University of Jyväskylä)
Regularity for a general class of discrete stochastic processes
In this talk, we consider an asymptotic regularity for expectations of a quite general class of discrete stochastic processes. Such expectations can also be described as solutions to a dynamic programming principles or as solutions to discretized PDEs. The result, which is also generalized to functions satisfying Puccitype inequalities for discrete extremal operators, can be seen as a counterpart to the KrylovSafonov regularity result in PDEs. However, the discrete step size has some crucial effects compared to the PDE setting. The proof combines analytic and probabilistic arguments. The result directly applies to a version of the tugofwar with noise.
This talk is partly based on a joint work with Ángel Arroyo and Pablo Blanc.
István Prause (Åbo Akademi University)
Lukas Schoug (University of Helsinki)
A first passage metric of the Gaussian free field
Paul Thevenin (Angers University)
Xilin Zhou (University of Jyväskylä)
Organizers
The workshop is hosted by the Department of Mathematics and Systems Analysis, Aalto University and organized by
Sponsors
Research Council of Finland (former Academy of Finland)
Finnish Centre of Excellence in Randomness and Structures (FiRSt)
Department of Mathematics and Systems Analysis, School of Science, Aalto University
Page content by: webmastermath [at] list [dot] aalto [dot] fi