BUDAPEST-VIENNA PROBABILITY SEMINAR
This series of events is jointly organised by the community of probabilists -- in a very wide sense -- of Vienna (IST, TUW, UW) and Budapest (BME, ELTE, RI). The informal group of organisers consists (right now) of: Mathias Beiglböck, Nathanael Berestycki, László Erdős, Jan Maas, Miklós Rásonyi, Gábor Pete, Fabio Toninelli and Bálint Tóth.
The events will be held quasi-regularly, with one or two meetings per semester, consisting of three 50 minutes lectures. The location of the events will alternate between the two cities. All are welcome!
The first, inaugural, event was held in Budapest, at the Rényi Institute, on Friday, 6th of March 2020.
2020-03-06
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Please note the last minute changes in the program (these are not unrelated): Nina Holden has cancelled her travel. István Berkes (RI) will speak in the second slot. Nathanael Berestycki changed topics.
THE TALKS:
14:00-14:50
NATHANAEL BERESTYCKI (Uni Wien): Random walks on planar maps and Liouville Brownian motion
Abstract: The study of random walks on random planar maps was initiated in a series of seminal papers of Benjamini and Schramm at the end of the 90s, motivated by contemporary (non-rigourous) works in the study of Liouville Quantum Gravity (LQG). Both topics have been the subject of intense research following remarkable breakthroughs in the last few years. After reviewing some of the recent developments in these fields - including Liouville Brownian motion, a canonical notion of diffusion on LQG surfaces - I will describe some joint work in progress with Ewain Gwynne. In this work we show that random walks on certain models of random planar maps (known as mated-CRT planar maps) have a scaling limit given by Liouville Brownian motion. This is true whether the maps are embedded using SLE/LQG theory or more intrinsically using the Tutte embedding. This is the first result confirming that Liouville Brownian motion is the scaling limit of random walks on planar maps. The proof relies on some earlier work of Gwynne, Miller and Sheffield which proves convergence to Brownian motion, modulo time-parametrisation. As an intermediate result of independent interest, we derive an axiomatic characterisation of Liouville Brownian motion, for which the notion of Revuz measure of a Markov process plays a crucial role.
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15:00-15:50
ISTVÁN BERKES (RI Budapest): Random walks on the circle and Diophantine approximation
Abstract: Let X1, X2, ... be i.i.d. lattice random variables with an irrational span α and let Sn =X1+...+Xn (mod 1). We show that the asymptotic properties of the random walk {Sn, n=1, 2, ...} are closely connected with the rational approximation properties of α and in particular, we point out an interesting critical phenomenon, i.e. a sudden change in the convergence speed in limit theorems for Sn as the Diophantine rank of α passes through a certain critical value.
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16:30-17:20
BALÁZS RÁTH (TU Budapest=BME): On the threshold of spread-out contact process percolation
Abstract: In the (spread-out) d-dimensional contact process, vertices can be healthy or infected. With rate one infected sites recover, and with rate lambda they transmit the infection to some other vertex chosen uniformly within a ball of radius R. In configurations sampled from the upper stationary distribution, we study nearest-neighbor site percolation of the set of infected sites and describe the asymptotic behaviour of the associated percolation threshold as R tends to infinity. Joint work with Daniel Valesin.
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DINNER:
After the seminar talks we will go out for dinner (going dutch) to some local restaurant. If you plan to join please do inform the local organizers (Gábor and/or Bálint) about this by Monday, 2nd of March.
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MAPS, DIRECTIONS:
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HOW TO GET TO THE RÉNYI INSTITUTE?
The Rényi Institute is in the very centre of the city. Trains from Vienna arrive at Keleti Station (rather central) with an earlier stop at Kelenföld Station (not so central). The RI is easily accessible from either of these using public transport . Kelenföld is further out, but time-wise it could be faster to get off the train there and take the metro/underground (M4) or the tram (49) as indicated below.
Here is how to come to the RI using public transport:
From Kelenföld Railway Station
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HOTELS NEARBY THE RÉNYI INSTITUTE:
Participants who wish to stay overnight in Budapest are kindly asked to make their own arrangements for accommodation.
Click here for hotels and hostels nearby the Rényi Institute (on Google maps).