2023-03-17
2023-03-17
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THE TALKS:
14:00-14:50
Abstract: It is well known that eigenvalues of general non-Hermitian matrices can be very unstable under tiny perturbations but adding a small noise regularises this instability. The quantity governing this effect, called the eigenvalue condition number in numerical linear algebra, is also well known in random matrix theory as the eigenvector overlap. We present several recent results on almost optimal lower and upper bounds on this key quantity. For the lower bound we need to prove the strong form of quantum unique ergodicity (QUE) for the singular vectors of non-Hermitian random matrices. The upper bound requires very different tools: here we prove a Wegner type estimate for non-Hermitian matrices. The talk is based upon joint works with G. Cipolloni, J. Henheik, H.-C. Ji, O. Kolupaiev and D. Schroder.
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15:00-15:50
LIHAN WANG (MPI Leipzig): The Gaussian free-field as a stream function: asymptotics of effective diffusivity in infra-red cut-off
Abstract: We investigate the effective diffusivity of a random drift-diffusion operator that is at the borderline of standard stochastic homogenization theory: In two space-dimensions, we consider the divergence-free drift with stream function given by the Gaussian free-field, with an ultra-violet cut-off at scale unity and an infra-red cut-off at a scale L. We establish the precise scaling of how the effective diffusivity diverges in terms of L, specifying recent results based on a Wiener chaos decomposition and a mathematical physics-type analysis in the corresponding Fock space. This amounts to the study of convection-enhanced diffusion at the borderline to anomalous diffusion. As a byproduct, we improve on the result by Cannizzaro, Haunschmid-Sibitz and Toninelli by removing the double logarithmic factor. Joint work with Georgiana Chatzigeorgiou, Peter Morfe and Felix Otto (MPI)
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16:30-17:20
PÉTER KEVEI (Bolyai Institute, Szeged): On the solution to the stochastic heat equation with Lévy noise
Abstract: We examine the almost sure asymptotics of the solution to the stochastic heat equation driven by a Lévy space-time white noise. For fixed time and space we determine the exact tail behavior of the solution. When a spatial point is fixed and time tends to infinity, we show that the solution develops unusually high peaks over short time intervals, even in the case of additive noise, which leads to a breakdown of an intuitively expected strong law of large numbers. We also determine the almost sure growth rate in space for fixed time. This is joint work with Carsten Chong (Columbia University).
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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, 13th 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).