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, Nathanaël Berestycki, László Erdős, Jan Maas, Miklós Rásonyi, Gábor Pete, Fabio Toninelli and Bálint Tóth.

The events are 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 Budapest and Vienna. All are welcome!

(Due to the pandemic, unfortunately, we had to modify our original plans. Hope to get back to normal soon.)

2022-04-27

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PLEASE NOTE THE LAST MINUTE CHANGE IN THE PROGRAM. UNFORTUNATELY HERBERT SPOHN (TU Munich) WILL NOT BE ABLE TO PRESENT HIS TALK. THIS WILL BE RESCHEDULED AT A LATER OCCASION.

THE TALKS:

14:00-14:50

GÁBOR PETE (Rényi Institute and TU Budapest): Stake-governed random tug-of-war

Abstract: Imagine a version of chess, where each player has 100 Forints, and, instead of alternating moves, before each turn they stake some portion of their fortunes, then flip a coin that is biased according to the stakes, and the winner of the coin toss makes the next move.
This would of course be too difficult to analyze mathematically. Instead, consider random tug-of-war on graphs, which is a probabilistic game that was introduced by Peres-Schramm-Sheffield-Wilson (JAMS 2009) to aid the analysis of the infinity-Laplace equation, a singular elliptic PDE. We introduce the stake-governed version of this game, and solve it on finite rooted trees, by finding the Nash equilibria for the stakes and moves. Joint work with Alan Hammond.

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15:00-15:50

MATHIAS BEIGLBÖCK (University of Vienna): The Wasserstein space of stochastic processes

Abstract: Wasserstein distance induces a natural Riemannian structure for the probabilities on the Euclidean space. This insight of classical transport theory is fundamental for tremendous applications in various fields of pure and applied mathematics.
We believe that an appropriate probabilistic variant, the adapted Wasserstein distance AW, can play a similar role for the class FP of filtered processes, i.e. stochastic processes together with a filtration. In contrast to other topologies for stochastic processes, probabilistic operations such as the Doob-decomposition, optimal stopping and stochastic control are continuous w.r.t. AW. We also show that (FP,AW) is a geodesic space, isometric to a classical Wasserstein space, and that martingales form a closed geodesically convex subspace. (Joint work with Daniel Bartl and Gudmund Pammer)

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16:30-17:20

OPEN PROBLEMS AND SHORT PRESENTATIONS:

Participants are encouraged to present interesting open problems in the format of a \le 10 min informal blackboard presentation.

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DINNER:

After the seminar talks we will go out for dinner to a local restaurant. If you plan to join please inform JD Kosche (jd.kosche@univie.ac.at) by Monday, 25 April 2022.

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DIRECTIONS:

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HOW TO GET TO IST AUSTRIA?

IST Austria is located in Klosterneuburg, north of Vienna. You can get there by public transport, car or bicycle.

Public transport: take the U4 to Heiligenstadt, then take either the IST shuttle bus or Bus 400 to stop "Institute of Science and Technology Austria (ISTA)"

For directions on how to get there by car or bicycle, please click here.

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WHERE TO STAY:

Participants who wish to stay overnight in Vienna are kindly asked to make their own arrangements for accommodation. Some hotels close to the U4 are: Pension Ani-falstaff, Hotel Bombolo, Hotel Boltzmann, Hotel & Palais Strudlhof

You can also stay at the IST Austria guesthouse, although space is limited. To make a reservation, please contact Birgit Oosthuizen-Noczil (birgit.oosthuizen-noczil@ist.ac.at) asap!

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