Departement Mathematik

Seminar on stochastic processes

Members of the probability group are involved in co-organizing remote specialized seminars that take place on Tuesdays and Thursdays:

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Frühjahrssemester 2013

Datum / Zeit Referent:in Titel Ort
20. Februar 2013
17:15-19:00 		Serguei Popov
University of Campinas
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Seminar on Stochastic Processes

Titel Soft local times and decoupling of random interlacements
Referent:in, Affiliation Serguei Popov, University of Campinas
Datum, Zeit 20. Februar 2013, 17:15-19:00
Ort Y27 H 25
Abstract We establish a decoupling feature of the random interlacement process I^u in Z^d, at level u, for d \geq 3. Roughly speaking, we show that observations of I^u restricted to two disjoint subsets A_1 and A_2 of Z^d are approximately independent, once we add a sprinkling to the process I^u by slightly increasing the parameter u. Our results differ from previous ones in that we allow the mutual distance between the sets A_1 and A_2 to be much smaller than their diameters. We then provide an important application of this decoupling for which such flexibility is crucial. More precisely, we prove that, above a certain critical threshold u**, the probability of having long paths that avoid I^u is exponentially small, with logarithmic corrections for d=3. To obtain the above decoupling, we first develop a general method for comparing the trace left by two Markov chains on the same state space. This method is based in what we call the soft local time of a chain. In another crucial step towards our main result, we also prove that any discrete set can be "smoothened" into a slightly enlarged discrete set, for which its equilibrium measure behaves in a regular way. This is a joint work with Augusto Teixeira.
Soft local times and decoupling of random interlacementsread_more
Y27 H 25
27. Februar 2013
17:15-19:00 		Zhan Shi
Université Paris VI
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Seminar on Stochastic Processes

Titel Branching random walks and martingales
Referent:in, Affiliation Zhan Shi, Université Paris VI
Datum, Zeit 27. Februar 2013, 17:15-19:00
Ort Y27 H 25
Abstract Branching random walks are often studied by means of some naturally associated martingales. I will make a few simple discussions on these martingales. Joint work with Elie Aïdékon.Branching random walks are often studied by means of some naturally associated martingales. I will make a few simple discussions on these martingales. Joint work with Elie Aïdékon.
Branching random walks and martingalesread_more
Y27 H 25
6. März 2013
17:15-19:00 		Omer Angel
University of British Columbia
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Seminar on Stochastic Processes

Titel Half planar random maps
Referent:in, Affiliation Omer Angel, University of British Columbia
Datum, Zeit 6. März 2013, 17:15-19:00
Ort Y27 H 25
Abstract Certain half planar random maps enjoy a certain "domain Markov" property. I will explore this property, describing work with Gourab Ray, as well as an application of this property to study exponents for critical percolation on several models of random planarmaps (work with Nicolas Curien).
Half planar random mapsread_more
Y27 H 25
13. März 2013
17:15-19:00 		Ralph Neininger
J.W. Goethe-Universität
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Seminar on Stochastic Processes

Titel On a functional contraction method
Referent:in, Affiliation Ralph Neininger, J.W. Goethe-Universität
Datum, Zeit 13. März 2013, 17:15-19:00
Ort Y27 H 25
Abstract Motivated by a problem from the probabilistic analysis of algorithms a functional version of the contraction method is presented. The average case analysis of the complexity of certain search operations (partial match queries) in data structures for multidimensional data (quad trees, K-d trees) was started in the 80s and 90s by Philippe Flajolet and co-authors. Probabilistic results regarding variances and limit distributions remained open due to peculiar dependencies. Results in this direction are presented based on a process convergence result of refined complexity measures. For this a functional version of the contraction method is developed based on the use of the Zolotarev metric on the space D[0,1]. The talk is based on joint work with Henning Sulzbach, http://arxiv.org/abs/1202.1370, and with Nicolas Broutin and Henning Sulzbach, http://arxiv.org/abs/1202.1342.
On a functional contraction methodread_more
Y27 H 25
20. März 2013
17:15-19:00 		Grégory Miermont
École Normale Supérieure de Lyon
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Seminar on Stochastic Processes

Titel Scaling limits of random maps in higher genera
Referent:in, Affiliation Grégory Miermont, École Normale Supérieure de Lyon
Datum, Zeit 20. März 2013, 17:15-19:00
Ort Y27 H 25
Abstract A map is an embedding of a 2-dimensional graph into a surface, which can be seen as a discrete geometrization of the latter. Therefore, it is natural to view a random map as a discrete random surface, which naturally leads to the question of the existence of a continuum counterpart obtained by passing to the limit after a suitable rescaling of the graph distances in the map. The planar case, where the surface is the 2-dimensional sphere, has been quite thoroughly studied in the past year. In this work in collaboration with Jérémie Bettinelli, we investigate other topologies by characterizing the scaling limits of uniform random plane quadrangulation with a boundary, or uniform bipartite quadrangulations in a closed, compact, orientable surface of fixed genus g. We achieve this by using "surgical" methods, that give a description of the scaling limits in terms of a gluing of elementary planar pieces.
Scaling limits of random maps in higher generaread_more
Y27 H 25
27. März 2013
17:15-18:15 		Jean-Christophe Mourrat
EPF Lausanne
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Seminar on Stochastic Processes

Titel Aging of spin glasses: the case of the random energy model
Referent:in, Affiliation Jean-Christophe Mourrat, EPF Lausanne
Datum, Zeit 27. März 2013, 17:15-18:15
Ort Y27 H 25
Abstract Physically, glassy systems are characterized by the phenomenon of aging: over every time-scale accessible to the experiment, the properties of the system evolve without reaching equilibrium. In this talk, we will focus on possibly the most basic mean-field model of a spin glass, called the random energy model. I will begin by describing heuristics that enable to predict the aging properties of dynamics on this model. I will then present recent rigorous results confirming these heuristics, which hold for a large class of natural dynamics. (Joint work with Pierre Mathieu.)
Aging of spin glasses: the case of the random energy modelread_more
Y27 H 25
10. April 2013
17:15-18:15 		Prof. Dr. Sergey Foss
Heriot-Watt University
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Seminar on Stochastic Processes

Titel Limit theorems for a random directed graph
Referent:in, Affiliation Prof. Dr. Sergey Foss, Heriot-Watt University
Datum, Zeit 10. April 2013, 17:15-18:15
Ort Y27 H 25
Abstract We consider a stochastic directed graph on the integers whereby a directed edge between i and a larger integer j exists with probability p that may depend on the distance j-i, and there is no edges from bigger to smaller integers. Edge lengths L(i,j) may be constants or i.i.d. random variables. We introduce also a complementary "infinite bin" model. We study the asymptotics for the maximal path length in a long chunk of the graph. Under certain assumptions, the model has a regenerative structure, and the SLLN and the CLT follow. Otherwise, we obtain scaling laws and asymptotic distributions expressed in terms of a "continuous last-passage percolation" model on [0,1]. If time allows, we introduce multi-dimensional extensions of the models. The talk is based on joint papers with T Konstantopoulos (2003, MPRF), D. Denisov and T. Konstantopoulos (2012, AnnAP), J. Martin and Ph. Schmidt (AnnAP, to appear) and S. Zachary (Adv/JAP, to appear).
Limit theorems for a random directed graphread_more
Y27 H 25
17. April 2013
17:15-19:00 		Yvan Velenik
Université de Genève
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Seminar on Stochastic Processes

Titel On the phase transition of self-attracting polymers under stretching
Referent:in, Affiliation Yvan Velenik, Université de Genève
Datum, Zeit 17. April 2013, 17:15-19:00
Ort Y27 H 25
Abstract We consider a general class of self-attracting polymer models under stretching (or, equivalently, self-attracting random walks with drift). It is well-known that such models undergo a phase transition as the intensity of the stretching force increases: at weak intensity, the polymer has a vanishing macroscopic extension (collapsed phase), while above a critical intensity, the polymer acquires a nonzero macroscopic extension (stretched phase). In dimensions 2 and above, this phase transition turns out to be always of first order, the macroscopic extension of the polymer, as a function of the intensity of the stretching force, being discontinuous at the transition. Moreover, at criticality the polymer still has a nonvanishing macroscopic extension, with Gaussian fluctuations. The talk is based on a joint work with Dmitry Ioffe [Self-Attractive Random Walks: The Case of Critical Drifts, Commun. Math. Phys. 313, 209-235 (2012)].
On the phase transition of self-attracting polymers under stretchingread_more
Y27 H 25
24. April 2013
17:15-18:15 		Dr. David Croydon
University of Warwick
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Seminar on Stochastic Processes

Titel Biased random walks on random paths and critical random trees
Referent:in, Affiliation Dr. David Croydon, University of Warwick
Datum, Zeit 24. April 2013, 17:15-18:15
Ort Y27 H 25
Abstract In this talk, I will discuss two problems that are motivated by understanding how biased random walks behave on large critical percolation clusters. Firstly, I will describe how introducing a bias slows down random walks on critical Galton-Watson branching process trees (this is joint work with Alexander Fribergh, New York University, and Takashi Kumagai, Kyoto University). Secondly, I consider the biased random walk on the range of a random walk. In this setting, I indicate how a localisation result can be proved by adapting techniques originally developed for one-dimensional random walks in random environments in Sinai's regime. In both settings, it is possible to make a precise statement about how the increasing the strength of the bias affects the long-time behaviour of the associated random walk.
Biased random walks on random paths and critical random treesread_more
Y27 H 25
15. Mai 2013
17:15-18:15 		Leif Döring
Universität Zürich
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Seminar on Stochastic Processes

Titel On General Random Interlacements and Processes Issued from Infinity
Referent:in, Affiliation Leif Döring, Universität Zürich
Datum, Zeit 15. Mai 2013, 17:15-18:15
Ort Y27 H 25
Abstract We will discuss random interlacements for general Markov processes seen from two perspectives: Either defined in an abstract Gibbsian setup or via a known two-sided procedure. Links to abstract Martin boundaries and probabilistic potential theory are given and a similar construction for some Markov processes issued from infinity are discussed.
On General Random Interlacements and Processes Issued from Infinityread_more
Y27 H 25
22. Mai 2013
17:15-19:00 		Reda Chhaibi
Universität Zürich
Details

Seminar on Stochastic Processes

Titel The geometric Robinson-Schensted correspondence and the Whittaker process for crystallographic root systems
Referent:in, Affiliation Reda Chhaibi, Universität Zürich
Datum, Zeit 22. Mai 2013, 17:15-19:00
Ort Y27 H 25
Abstract The Robinson-Schenstend correspondence is originally a bijection between words and pairs of tableaux. It can be used to define a dynamic on partition called the Schur process. A diffusive limit of the Schur process gives Dyson's Brownian motion. Here, we will present a "geometric Robinson-Schensted correspondence". by taking Brownian motion as input, one finds the Whittaker process, which can be seen as an integrable system of weakly repulsive particles. The construction works in the full generality of arbitrary crystallographic root systems.
The geometric Robinson-Schensted correspondence and the Whittaker process for crystallographic root systemsread_more
Y27 H 25
29. Mai 2013
16:00-17:00 		Hugo Duminil-Copin
Université de Genève
Details

Seminar on Stochastic Processes

Titel Absence of percolation for critical Bernoulli percolation on planar slabs
Referent:in, Affiliation Hugo Duminil-Copin, Université de Genève
Datum, Zeit 29. Mai 2013, 16:00-17:00
Ort Y27 H 25
Abstract We prove that the probability that there exists an infinite cluster for critical Bernoulli percolation on Z^2times G for any finite graph G is equal to zero. As a byproduct of the proof, we show that finite range percolation on Z^2 does not percolate at criticality (some symmetry is required for the interactions). This talk is based on a joint work with V. Sidoravicius and V. Tassion.
Absence of percolation for critical Bernoulli percolation on planar slabsread_more
Y27 H 25
29. Mai 2013
17:15-18:15 		Ivan Corwin
MIT, USA
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Seminar on Stochastic Processes

Titel Integrable (stochastic) interacting particle systems
Referent:in, Affiliation Ivan Corwin, MIT, USA
Datum, Zeit 29. Mai 2013, 17:15-18:15
Ort Y27 H 25
Abstract I will explain a general approach useful in solving a variety of (stochastic) interacting particle systems including ASEP, q-TASEP (continuous and discrete time versions), q-pushTASEP, O'Connell-Yor semi-discrete directed polymer, and the stochastic heat equation (or equivalently the Kardar-Parisi-Zhang equation). The approach involves finding observables of the systems whose expectations evolve according to closed (deterministic) integrable evolution equations which can, in turn, be explicitly solved. Connections to the theory of Macdonald processes, Bethe ansatz and the polymer replica method will be made as well.
Integrable (stochastic) interacting particle systemsread_more
Y27 H 25
5. Juni 2013
17:15-18:15 		Thierry Bodineau
ENS Paris
Details

Seminar on Stochastic Processes

Titel Metastability and interface motion in disordered media
Referent:in, Affiliation Thierry Bodineau, ENS Paris
Datum, Zeit 5. Juni 2013, 17:15-18:15
Ort Y27 H 25
Abstract We will first review the return to equilibrium of the Ising model when a small external field is applied. The relaxation time is extremely long and can be estimated as the time needed to create critical droplets of the stable phase which will invade the whole system. We will then discuss the impact of disorder on this metastable behavior and show that for Ising model with random interactions (dilution of the couplings) the relaxation time is much faster as the disorder acts as a catalyst. In the last part of the talk, we will focus on the droplet growth and study a toy model describing interface motion in disordered media.
Metastability and interface motion in disordered mediaread_more
Y27 H 25

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Organisatoren:innen: Jean Bertoin, Erwin Bolthausen, Ashkan Nikeghbali, Pierre Nolin, Martin Schweizer, Alain-Sol Sznitman

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