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X-WR-CALNAME:Probability Theory
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TZID:Europe/Zurich
X-LIC-LOCATION:Europe/Zurich
TZURL:http://tzurl.org/zoneinfo/Europe/Zurich
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TZOFFSETFROM:+0100
TZOFFSETTO:+0200
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DTSTART:19810329T020000
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DTSTART:19961027T030000
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BEGIN:VEVENT
UID:news355@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20181030T094303
DTSTART;TZID=Europe/Zurich:20181212T110000
SUMMARY:Seminar in probability theory: Ioan Manolescu (Fribourg)
DESCRIPTION:TBA
X-ALT-DESC:TBA
END:VEVENT
BEGIN:VEVENT
UID:news354@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20181030T094136
DTSTART;TZID=Europe/Zurich:20181128T110000
SUMMARY:Seminar in probability theory: Gaultier Lambert (University of Zuri
ch)
DESCRIPTION:TBA
X-ALT-DESC:TBA
END:VEVENT
BEGIN:VEVENT
UID:news326@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20181103T093011
DTSTART;TZID=Europe/Zurich:20181121T110000
SUMMARY:Seminar in probability theory: Antti Knowles (Geneva)
DESCRIPTION:We consider the adjacency matrix of the Erdos-Renyi graph G(N\,
p) in the supercritical regime pN > C log N for some universal constant C
. We show that the eigenvalue density is with high probability well appr
oximated by the semicircle law on all spectral scales larger than the typ
ical eigenvalue spacing. We also show that all eigenvectors are completel
y delocalized with high probability. Both results are optimal in the sens
e that they are known to be false for pN < log N. A key ingredient of the
proof is a new family of large deviation estimates for multilinear forms
of sparse vectors. \\r\\nJoint work with Yukun He and Matteo Marcozzi.
X-ALT-DESC: We consider the adjacency matrix of the Erdos-Renyi graph G(N\,
p) in the supercritical regime pN >\; C log N for some universal consta
nt C. We show that the eigenvalue density is with high probability well
approximated by the semicircle law on all spectral scales larger than the
typical eigenvalue spacing. We also show that all eigenvectors are compl
etely delocalized with high probability. Both results are optimal in the
sense that they are known to be false for pN <\; log N. A key ingredien
t of the proof is a new family of large deviation estimates for multiline
ar forms of sparse vectors. \nJoint work with Yukun He and Matteo Marcozz
i.
END:VEVENT
BEGIN:VEVENT
UID:news353@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20181103T092837
DTSTART;TZID=Europe/Zurich:20181114T110000
SUMMARY:Seminar in probability theory: Marius Schmidt (Basel)
DESCRIPTION:Consider the hypercube as a graph with vertex set {0\,1}^N and
edges between two vertices if they are only one coordinate flip apart. C
hoosing independent standard exponentially distributed lengths for all ed
ges and asking how long the shortest directed paths from (0\,..\,0) to (1
\,..\,1) is defines oriented first passage percolation on the hypercube.
We will discuss the conceptual steps needed to answer this question to th
e precision of extremal process following the two paper series "Oriented
first passage percolation in the mean field limit" by Nicola Kistler\, Ad
rien Schertzer and Marius A. Schmidt: arXiv:1804.03117 and arXiv:1808.0459
8.
X-ALT-DESC: Consider the hypercube as a graph with vertex set {0\,1}^N and
edges between two vertices if they are only one coordinate flip apart. C
hoosing independent standard exponentially distributed lengths for all ed
ges and asking how long the shortest directed paths from (0\,..\,0) to (1
\,..\,1) is defines oriented first passage percolation on the hypercube.
We will discuss the conceptual steps needed to answer this question to th
e precision of extremal process following the two paper series "\;Ori
ented first passage percolation in the mean field limit"\; by Nicola
Kistler\, Adrien Schertzer and Marius A. Schmidt: arXiv:1804.03117 and arX
iv:1808.04598.
END:VEVENT
BEGIN:VEVENT
UID:news352@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20181103T092627
DTSTART;TZID=Europe/Zurich:20181107T110000
SUMMARY:Seminar in probability theory: Dominik Schröder (IST Austria)
DESCRIPTION:For Wigner-type matrices\, i.e. Hermitian random matrices with
independent\, not necessarily identically distributed entries above the
diagonal\, we show that at any cusp singularity of the limiting eigenvalu
e distribution the local eigenvalue statistics are universal and form a P
earcey process. Since the density of states typically exhibits only squar
e root or cubic root cusp singularities\, our work complements previous r
esults on the bulk and edge universality and it thus completes the resolu
tion of the Wigner-Dyson-Mehta universality conjecture for the last remai
ning universality type.
X-ALT-DESC: For Wigner-type matrices\, i.e. Hermitian random matrices with
independent\, not necessarily identically distributed entries above the
diagonal\, we show that at any cusp singularity of the limiting eigenvalu
e distribution the local eigenvalue statistics are universal and form a P
earcey process. Since the density of states typically exhibits only squar
e root or cubic root cusp singularities\, our work complements previous r
esults on the bulk and edge universality and it thus completes the resolu
tion of the Wigner-Dyson-Mehta universality conjecture for the last remai
ning universality type.
END:VEVENT
BEGIN:VEVENT
UID:news327@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20181030T093900
DTSTART;TZID=Europe/Zurich:20181031T110000
SUMMARY:Seminar in probability theory: Anton Klimovsky (Duisburg-Essen)
DESCRIPTION:Finding the (space-height) distribution of the (local) extrema
of high-dimensional strongly correlated random fields is a notorious hard
problem with many applications. Following Fyodorov & Sommers (2007)\, we f
ocus on the Gaussian fields with isotropic increments and take the viewpoi
nt of statistical physics. By exploiting various probabilistic symmetries\
, we rigorously derive the Fyodorov-Sommers formula for the log-partition
function in the high-dimensional limit. The formula suggests a rich pictur
e for the distribution of the local extrema akin to the celebrated spheric
al Sherrington-Kirkpatrick model with mixed p-spin interactions.
X-ALT-DESC: Finding the (space-height) distribution of the (local) extrema
of high-dimensional strongly correlated random fields is a notorious hard
problem with many applications. Following Fyodorov &\; Sommers (2007)\,
we focus on the Gaussian fields with isotropic increments and take the vi
ewpoint of statistical physics. By exploiting various probabilistic symmet
ries\, we rigorously derive the Fyodorov-Sommers formula for the log-parti
tion function in the high-dimensional limit. The formula suggests a rich p
icture for the distribution of the local extrema akin to the celebrated sp
herical Sherrington-Kirkpatrick model with mixed p-spin interactions.
END:VEVENT
BEGIN:VEVENT
UID:news325@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20180925T212513
DTSTART;TZID=Europe/Zurich:20180906T110000
SUMMARY:Seminar in probability theory: Lisa Hartung (New York University)
DESCRIPTION:It was proven by Rider and Virag that the logarithm of the char
acteristic polynomial of the Ginibre ensemble converges to a logarithmical
ly correlated random field. In this talk we will see how this connection c
an be established on the level if powers of the characteristic polynomial
by proving convergence to Gaussian multiplicative chaos. We consider the r
ange of powers in the L^2 phase. \\r\\n(Joint work in progress with Paul B
ourgade and Guillaume Dubach).
X-ALT-DESC: It was proven by Rider and Virag that the logarithm of the char
acteristic polynomial of the Ginibre ensemble converges to a logarithmical
ly correlated random field. In this talk we will see how this connection c
an be established on the level if powers of the characteristic polynomial
by proving convergence to Gaussian multiplicative chaos. We consider the r
ange of powers in the L^2 phase. \n(Joint work in progress with Paul Bourg
ade and Guillaume Dubach).
DTEND;TZID=Europe/Zurich:20180906T120000
END:VEVENT
BEGIN:VEVENT
UID:news306@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20180927T122021
DTSTART;TZID=Europe/Zurich:20180822T110000
SUMMARY:Seminar in probability theory: Alexander Drewitz (Köln)
DESCRIPTION:We consider two fundamental percolation models with long-range
correlations: The Gaussian free field and (the vacant set) of Random Inter
lacements. Both models have been the subject of intensive research during
the last years and decades\, on Zd as well as on some more general graphs.
We investigate some structural percolative properties around their critic
al parameters\, in particular the ubiquity of the infinite components of c
omplementary phases. \\r\\nThis talk is based on joint works with A. Prév
ost (Köln) and P.-F. Rodriguez (Bures-sur-Yvette).
X-ALT-DESC: We consider two fundamental percolation models with long-range
correlations: The Gaussian free field and (the vacant set) of Random Inter
lacements. Both models have been the subject of intensive research during
the last years and decades\, on Zd as well as on some more general graphs.
We investigate some structural percolative properties around their critic
al parameters\, in particular the ubiquity of the infinite components of c
omplementary phases. \nThis talk is based on joint works with A. Prévost
(Köln) and P.-F. Rodriguez (Bures-sur-Yvette).
DTEND;TZID=Europe/Zurich:20180822T120000
END:VEVENT
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