Tuesdays 4.30-5.30 pm,
MR 12.
|
| Date | Speaker | Title | Notes |
| 3 May | James Norris (Cambridge) | Aggregation and Coalescence I (abstract) | |
| 10 May | James Norris (Cambridge) | Aggregation and Coalescence II (abstract) | Note: 3pm |
| 10 May | Guenter Last (Karlsruhe Institute of Technology) | Old and new results on stationary tessellations (abstract) | |
| 17 May | James Norris (Cambridge) | Aggregation and Coalescence III (abstract). | |
| 24 May | Raphael Roux (Dauphine) | Probabilistic Euler Scheme for Fractional Conservational Laws (abstract). | |
| 31 May | Jason Schweinsberg (UCSD) | Dynamics of the evolving Bolthausen-Sznitman coalescent (abstract). | |
| 9 June | Po-Shen Loh (Carnegie-Mellon) | Connectivity in discrete random processes (abstract). | Note unusual day (Thursday). |
| 14 June | Thorsten Rheinlander | Symmetric processes and Ocone martingales (abstract) |
I will present some facts about propagation of chaos for a system of
particles driven by jump processes and interacting through their empirical
distribution function.
The system I will consider is designed in such a way that the limit process
should satisfies the fractional conservation law, which is a nonlinear
partial differential equation with nonlocal diffusion.
I will present different convergence results about the system, depending of
the distribution of the jumps. In particular, the associated Euler scheme
allows to simulate the solution to the fractional conservation law.
Recently, motivated by the practical problem of establishing
connectivity in peer-to-peer networks, a natural question of similar
flavor arose in the analysis of a natural randomized clustering
algorithm. Using methods which originated from physics, but now known
to be remarkably useful in the study of random graphs, we establish
the asymptotic optimality of this algorithm. We also prove the first
rigorous lower bounds on the performance of a closely-related
algorithm, extending an approach of Oded Schramm.
James Norris, Aggregation and Coalescence. Abstract:
These talks will aim to give an introduction to recent work (joint
with Amanda Turner) on
some models for planar random growth, which are encoded in terms of
compositions of
conformal maps. Properties of the evolving aggregation cluster will be
derived for the
asymptotic of small particle size and long time. A link will be
demonstrated with the coalescing
Brownian flow on the circle which eventually allows us to describe a non-trivial
internal random tree structure for the clusters.
10 May, Guenter Last. Old and new results on stationary tessellations. Abstract:
In the first part of the talk we present a few fundamental properties
of stationary tessellations of Euclidean space.
Then we proceed with more recent distributional
results on Poisson Voronoi and Poisson hyperplane
tessellations. Finally we propose
three models for continuum percolation
on planar tessellations.
24 May, Raphael Roux. Probabilistic Euler Scheme for Fractional Conservational Laws. Abstract:
31 May, Jason Schweinsberg. Dynamics of the evolving Bolthausen-Sznitman
coalescent. Abstract:
Consider a population of fixed size that
evolves over time. At each time, the genealogical
structure of the population can be described by a
coalescent tree whose branches are traced back to
the most recent common ancestor of the population.
This gives rise to a tree-valued stochastic process,
known as the evolving coalescent. We will study this
process in the case of populations whose genealogy is
given by the Bolthausen-Sznitman coalescent. We will
focus on the evolution of the time back to the most
recent common ancestor and the total length of
branches in the tree.
9 June, Po-Shen Loh. Connectivity in discrete random processes. Abstract:
Half a century ago, a seminal paper of Erdos and Renyi launched the
systematic study of random graphs. Since then, this direction of
investigation has blossomed into a broad field, and the original model
has given rise to many useful variants. Of the properties which have
received attention, one of the most fundamental has been that of
global connectivity.