Probability laboratory at Bath

Seminar abstracts

Our seminars are usually held on Mondays at 12.15pm in room 4W 1.7. If you wish to find out more, please contact Alexandre Stauffer or one of the other members of the group.

2nd October 2017 - Jean-Francois Marckert (Université de Bordeaux)

Some news concerning coalescing processes
Consider at time 0, a family of n particles with mass 1. These masses coalesce according to the following rule: each pair of masses (m,m') coalesces when a random clock following an exponential distribution with parameter K(m,m') rings, where the kernel K is the main parameter of the model. When coalescence occurs the pair of mass (m,m') is replaced by a single mass m+m', and the clocks are updated.
When the kernel is additive (K(m,m')=m+m') or multiplicative (K(m,m')=mm') these processes possesses some combinatorial representations which allows one to prove scaling limit for the evolution of mass distribution when n goes to +infinity (Aldous, Pitman, Chassaing, Louchard, Bertoin...)
The aim of this talk is to present "old" combinatorial encodings of these processes, as well as new ones. We will see that minor modifications of the encodings allows to get much richer combinatorial environments, allowing to get new asymptotic results.
This is based on joint works with Nicolas Broutin and Minmin Wang.

9th October 2017 - Thierry Bodineau (École Polytechnique)

Large time asymptotics of a hard sphere gas close to equilibrium
We consider a tagged particle in a diluted gas of hard spheres. Starting from the hamiltonian dynamics of particles in the Boltzmann-Grad limit, we will show that the tagged particle follows a Brownian motion after an appropriate rescaling. We also discuss the convergence of the motion of a big tagged particle towards a Langevin process.

16th October 2017 - Ioan Manolescu (Université de Fribourg)

First order phase transition for the Random Cluster model with q > 4
This talk aims to prove that the phrase transition of the planar random cluster model (and that of the associated Potts model) is discontinuous when q > 4. The result is obtained by computing rigorously the correlation length of the critical RCM using a correspondence with the six vertex model. The latter may be expressed using the transfer matrix formalism; the Perron-Frobenius eigenvalues of the diagonal blocks of the transfer matrix may then be computed using the Bethe ansatz.

23rd October 2017 - Denis Villemonais (École des Mines de Nancy)

Non-failable approximation method for conditioned distributions
We present a new approximation method for conditional distributions, which is non-failable and, under mild conditions, which converges uniformly in time. Our results are illustrated by their application to a neutron transport model. This is a joint work with William Oçafrain.

30th October 2017 - Timothy Budd (Université Paris-Saclay)

Nesting of loops versus winding of walks
Random planar maps with a boundary coupled to an O(n) loop model are expected, upon uniformization, to scale towards Liouville Quantum Gravity (LQG) in the unit disk together with an independent Conformal Loop Ensemble (CLE). This expectation was corroborated by work of Borot, Bouttier & Duplantier in which they found that the asymptotic nesting statistics of loops on the planar map side was related through a Knizhnik-Polyakov-Zamolodchikov (KPZ) relation to the equivalent for CLE obtained by Miller, Watson & Wilson. In this talk I will show that the nesting on the planar map side is closely related, even at the combinatorial level, to another random process in the plane: the winding of two-dimensional random walks around the origin. Inspection of the scaling limit of the latter in terms of Brownian motion sheds some light on the appearance of the KPZ relation.

6th November 2017 - Henning Sulzbach (University of Birmingham)

Galton-Watson trees and Apollonian networks
In the analysis of critical Galton-Watson trees conditional on their sizes, two complementary approaches have proved fruitful over the last decades. First, the so-called size-biased tree allows the study of local properties such as node degrees. Second, the global scaling limit, the Continuum Random tree, provides access to the study of average or extreme node depths. In this talk, I will discuss the approximation of the tree by subtrees with bounded node degrees. Here, the so-called "heavy subtrees" play an important role. An application will be given in terms of uniform Apollonian networks. The talk is based on joint work with Luc Devroye (McGill, Montreal) and Cecilia Holmgren (Uppsala).

9th November 2017 - Wioletta Ruszel (Technical University Delft)

Odometers and bi-Laplacian fields - Note: this seminar is on a Thursday
The divisible sandpile model is a special case of the class of continuous fixed energy sandpile models on some lattice or graph where the initial configuration is random and the evolution deterministic. One question which arises is under which conditions the model will stabilize or not. The amount of mass u(x) emitted from a certain vertex x during stabilization is called the odometer function. In this talk we will construct the scaling limit of the odometer function of a divisible sandpile model on a torus and show that it it converges to a continuum bi-Laplacian field.
This is joint work with A. Cipriani (U Bath) and R. Hazra (ISI Kolkatta).

13th November 2017 - Fredrik Viklund (KTH, Sweden)

TBA
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27th November 2017 - Giuseppe Cannizzaro (Imperial College London)

TBA
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4th December 2017 - Pietro Siorpaes (Imperial College London)

TBA
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11th December 2017 - Eleanora Kreacic (University of Oxford)

TBA
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8th January 2018 - Jonathan Hermon (University of Cambridge)

TBA
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15th January 2018 - Stefan Junk (TU Munich)

TBA
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22nd January 2018 - Erich Baur (Bern University of Applied Sciences)

TBA
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5th February 2018 - Nicos Georgiou (University of Sussex)

TBA
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Past seminars

2016/17: Winter and Spring
2015/16: Winter and Spring
2014/15: Winter and Spring
2013/14: Winter and Spring
2012/13: Winter and Spring
2011/12: Winter and Spring
2010/11: Winter, Spring
2009/10: Winter, Spring
2008/9: Winter, Spring
2007/8: Winter, Spring
2006/7: Winter, Spring