Seminar on Probability Theory - summer term
2013
Time: Tuesday, 17:00-18:30
Room: C 2.09 (Mathematik), UZA4,
Nordbergstraße 15, 2.OG
Organizer: Jiří Černý
First meeting: Tuesday, 12 March 2013,
17:00-18:30
| Date: | Speaker: | Title : |
| Tue, 19 March 17:00-18:30 |
Jean-Christophe Mourrat (EPFL) | Aging of spin glasses: the case of the random energy model |
| 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 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.) | ||
| Tue, 16 April 17:00-18:30 |
David Croydon (Warwick) |
Biased random walks on random paths and critical random trees |
| 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. | ||
| Tue, 30 April 17:00-18:30 |
Elisabeth Prossinger | Upper bounds on mixing time of Markov chains |
| Student presentation | ||
| Tue, 7 May 17:00-18:30 |
Magdalena Mujetic | Lower bounds on mixing time of Markov chains |
| Student presentation | ||
| Tue, 14 May 17:00-18:30 |
Fabian Pühringer | Cover times |
| Student presentation | ||
| Tue, 28 May 17:00-18:30 |
Florian Stebegg | TBA |
| Student presentation | ||
| Tue, June 11 17:00-18:30 |
Balázs
Ráth (UBC) |
On the geometry of correlated percolation models |
| Abstract:Let S
denote a random subset of the Z^d nearest neighbor
lattice. What do we need to assume about the law of S
so that we can infer that the geometry of the unique
infinite cluster of the subgraph spanned by S is
similar to that of Z^d? In my talk I outline a list
of "axioms" which imply the existence of a norm on
R^d such that the graph distance of far away vertices
in the infinite cluster of S can be well approximated
by their distance with respect to this norm. Our
axioms are not only satisfied by the well-known
Bernoulli percolation model, but also other, more
exotic models with long-range correlations, like the
vacant set of random interlacements and the level
sets of Gaussian free field. The talk is based on: Alexander Drewitz, Balázs Ráth, Artem Sapozhnikov: On chemical distances and shape theorems in percolation models with long-range correlations (2012, submitted) |
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| Tue, June 18 17:00-18:30 |
Jan
Swart (UTIA Prague) |
Rebellious voter models |
| Abstract: How
different should two closely related species be in
order to be able to coexist without one species
competing the other away? This biological question
leads to the study of voter models in which minority
types have an advantage and which are dual to systems
of parity preserving branching and annihilating
random walks. In this talk, I will review the modest
mathematical progress in the study of such models
that has been made in recent years and also mention
some questions that are not fully understood
mathematically or even on the level of nonrigorous
arguments. This is joint work with Anja Sturm (Göttingen) and Karel Vrbenský (Prague). |
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| Tue, June 25 17:00-18:30 |
Andrej Depperschmidt (Freiburg (D)) |
Tree-valued Fleming-Viot processes with mutation and selection |
| In population genetics
Moran models are used to describe the evolution of
types in a population of a fixed size $N$. The type
of individuals may change due to mutation.
Furthermore, due to selection the fitness (i.e.\ the
ability to survive and produce offspring) of an
individual depends on its current type. At fixed
times the genealogy of such populations can be
constructed using the ancestral selection graph (ASG)
of Krone and Neuhauser, which generalises the Kingman
coalescent. As the population evolves its genealogy evolves as well. In the talk we describe the construction of a tree-valued version of the Fleming-Viot process with mutation and selection (TFVMS) using a well-posed martingale problem. This extends the construction of the neutral tree-valued process given in (Greven, Pfaffelhuber and Winter, 2012). Furthermore we discuss properties of the TFVMS. In particular, as time permits, we show that some properties of the Kingman coalescent can be lifted to the tree-valued setting. |
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