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Seminar on Stochastic Processes

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Spring Semester 2019

Date / Time Speaker Title Location
20 February 2019
17:15-18:15 		Massimiliano Gubinelli
Universität Bonn
Event Details

Seminar on Stochastic Processes

Title Probabilistic aspects of the $Phi^4_3$ Euclidean Quantum Field Theory
Speaker, Affiliation Massimiliano Gubinelli, Universität Bonn
Date, Time 20 February 2019, 17:15-18:15
Location Y27 H 12
Abstract The $Phi^4_3$ Euclidean QFT is a non-Gaussian measure supported on distribution over a three dimensional finite or infinite domain which has applications to constructive quantum field theory. In this talk I will review recent work on the construction and characterisation of the $Phi^4_3$ Euclidean QFT via stochastic methods. In particular I will discuss a variational formula for its Laplace transform in a finite volume, its construction in infinite volume via PDE techniques and an integration by parts formula.
(Based on joint works with N. Barashkov and M. Hofmanova).
Probabilistic aspects of the $Phi^4_3$ Euclidean Quantum Field Theoryread_more
Y27 H 12
27 February 2019
17:15-18:15 		Tyler Helmuth
University of Bristol
Event Details

Seminar on Stochastic Processes

Title Spin systems, isomorphism theorems, and random walks
Speaker, Affiliation Tyler Helmuth, University of Bristol
Date, Time 27 February 2019, 17:15-18:15
Location Y27 H 12
Abstract The classical isomorphism theorems are distributional identities that relate the local times of simple random walk to the square of the Gaussian free field (GFF). It is possible to see these relations as a consequence of the continuous translation symmetry of the GFF, and by using similar ideas it is possible to derive isomorphism theorems that relate the vertex-reinforced jump process to hyperbolic spin systems. I will explain how this works, and how the resulting identities can be used to prove the recurrence of the vertex-reinforced jump process on the two-dimensional square lattice.
Spin systems, isomorphism theorems, and random walksread_more
Y27 H 12
6 March 2019
17:15-18:15 		Armand Riera
Université Orsay
Event Details

Seminar on Stochastic Processes

Title Growth-fragmentation processes in Brownian motion indexed by the Brownian tree
Speaker, Affiliation Armand Riera, Université Orsay
Date, Time 6 March 2019, 17:15-18:15
Location Y27 H 12
Abstract Brownian motion indexed by the Brownian tree is the continuous analog of a random walk indexed by a critical Galton-Watson tree (with finite variance). It is directly related to the Super-Brownian motion and more surprisingly with Brownian geometry.
The goal of this talk is to present the positive excursion theory of Brownian motion indexed by the Brownian tree and to show that the genealogy of positive excursions is coded by a well-identified growth-fragmentation process. In the context of Brownian geometry, this means that if we slice a free Brownian disk at heights the same growth-fragmentation process encodes the perimeter of the resulting connected components. These connected components evolve, conditionally to their perimeters, as independent Brownian disks.
This talk is based on joint work with Jean-François Le Gall.
Growth-fragmentation processes in Brownian motion indexed by the Brownian treeread_more
Y27 H 12
20 March 2019
17:15-18:15 		Peter Mörters
Universität Köln
Event Details

Seminar on Stochastic Processes

Title Metastability of the contact process on evolving scale-free networks
Speaker, Affiliation Peter Mörters, Universität Köln
Date, Time 20 March 2019, 17:15-18:15
Location Y27 H 12
Abstract We study the contact process in the regime of small infection rates on scale-free networks evolving by stationary dynamics. A parameter allows us to interpolate between slow (static) and fast (mean-field) network dynamics. For two paradigmatic classes of networks we investigate transitions between phases of fast and slow extinction and in the latter case we analyse the density of infected vertices in the metastable state. The talk is based on joint work with Emmanuel Jacob (ENS Lyon) and Amitai Linker (Universidad de Chile).
Metastability of the contact process on evolving scale-free networksread_more
Y27 H 12
27 March 2019
17:15-18:15 		Denis Villemonais
Université de Nancy, France
Event Details

Seminar on Stochastic Processes

Title General criteria for the study of quasi-stationarity
Speaker, Affiliation Denis Villemonais , Université de Nancy, France
Date, Time 27 March 2019, 17:15-18:15
Location Y27 H 12
Abstract In this work in collaboration with Nicolas Champagnat (IECL, Nancy France), we provide a new set of criteria for proving the existence of quasi-stationary distributions for absorbed Markov processes typically evolving in non-compact spaces. The talk will go through the definition and basic properties of quasi-stationary distributions, the presentation of the above mention criteria and applications to perturbed dynamical systems, diffusion processes, measured valued Pólya processes (a collaboration with Cécile Mailler, Univeristy of Bath UK) and branching processes.
General criteria for the study of quasi-stationarityread_more
Y27 H 12
3 April 2019
17:15-18:15 		Thomas Budzinski
Université Orsay
Event Details

Seminar on Stochastic Processes

Title Local limits of uniform triangulations in high genus
Speaker, Affiliation Thomas Budzinski , Université Orsay
Date, Time 3 April 2019, 17:15-18:15
Location Y27 H 12
Abstract We study the local limits of uniform triangulations chosen uniformly over those with fixed size and genus in the regime where the genus is proportional to the size. We show that they converge to the Planar Stochastic Hyperbolic Triangulations introduced by Curien. This generalizes the convergence of uniform planar triangulations to the UIPT of Angel and Schramm, and proves a conjecture of Benjamini and Curien. As a consequence, we obtain new asymptotics on the enumeration of high genus triangulations. This is a joint work with Baptiste Louf.
Local limits of uniform triangulations in high genusread_more
Y27 H 12
10 April 2019
17:15-18:15
Event Details

Seminar on Stochastic Processes

Title Special session on some of Harry Kesten's mathematics, I
Speaker, Affiliation
Date, Time 10 April 2019, 17:15-18:15
Location Y27 H 12
Special session on some of Harry Kesten's mathematics, I
Y27 H 12
17 April 2019
17:15-18:15
Event Details

Seminar on Stochastic Processes

Title Special session on some of Harry Kesten's mathematics, II
Speaker, Affiliation
Date, Time 17 April 2019, 17:15-18:15
Location Y27 H 12
Special session on some of Harry Kesten's mathematics, II
Y27 H 12
8 May 2019
17:15-18:15 		Jeff Steif
Chalmers University
Event Details

Seminar on Stochastic Processes

Title Fortuin-Kastelyn representations for Threshold Gaussian and Stable Vectors: aka Divide and Color models
Speaker, Affiliation Jeff Steif, Chalmers University
Date, Time 8 May 2019, 17:15-18:15
Location Y27 H 12
Abstract We consider the following simple model: one starts with a finite (or countable) set V, a random partition of V and a parameter p in [0,1]. The "Generalized Divide and Color Model" is the {0,1}-valued process indexed by V obtained by independently, for each partition element in the random partition chosen, with probability p assigning all the elements of the partition element the value 1, and with probability 1−p, assigning all the elements of the partition element the value 0. Many models fall into this context:
(1) the 0 external field Ising model (where the random partition is given by FK percolation),
(2) the stationary distributions for the voter model (where the random partition is given by coalescing random walks),
(3) random walk in random scenery and
(4) the original "Divide and Color Model" introduced and studied by Olle Häggström.
In earlier work, Johan Tykesson studied what one could say about such processes. In joint work with Malin Palö Forsström, we study the question of which threshold Gaussian and stable vectors have such a representation: (A threshold Gaussian (stable) vector is a vector obtained by taking a Gaussian (stable) vector and a threshold h and looking where the vector exceeds the threshold h). The answer turns out to be quite varied depending on properties of the vector and the threshold; it turns out that h=0 behaves quite differently than h different from 0. Among other results, in the large h regime, we obtain a phase transition in the stability exponent alpha for stable vectors and the critical value is alpha=1.
Fortuin-Kastelyn representations for Threshold Gaussian and Stable Vectors: aka Divide and Color modelsread_more
Y27 H 12
22 May 2019
17:15-18:15 		Fredrik Wiklund
KTH, Stockholm
Event Details

Seminar on Stochastic Processes

Title CFT on the lattice: Virasoro relations and the critical Ising model
Speaker, Affiliation Fredrik Wiklund , KTH, Stockholm
Date, Time 22 May 2019, 17:15-18:15
Location Y27 H 12
Abstract Conformal field theory (CFT) is a powerful but non-rigorous approach to describing scaling limits of critical lattice models in the plane. CFT methods have been used to, e.g., predict exact formulas for correlation functions and values for critical exponents. For some models, some of the predictions can now be proved using discrete complex analysis and SLE techniques. A key structure in the CFT approach is the Virasoro algebra, an infinite dimensional Lie algebra. I will report on joint work with Clement Hongler and Kalle Kytölä that uses discrete complex analysis to construct a representation of the Virasoro algebra in terms of lattice fields of the critical Ising model, thereby tightly linking the principal exactly solvable structures for the lattice model and the CFT. Along the way I will also briefly review a corresponding result for the discrete Gaussian free field.
CFT on the lattice: Virasoro relations and the critical Ising modelread_more
Y27 H 12

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