# Colloquium in probability and other talks in summer term 2011

**Organizers:** Nina Gantert (TUM), Hans-Otto Georgii (LMU), Franz Merkl (LMU), Thomas Richthammer (LMU), Silke Rolles (TUM), Vitali Wachtel (LMU), Gerhard Winkler (Helmholtz Zentrum München)

**Talks:**

- Monday, 9.5.2011, 16:15, Room B251 at LMU.

Simon Aumann (LMU):*Zählmaß pivotaler Punkte*

**Abstract:**Es wird der Artikel "Pivotal, cluster and interface measures for critical planar percolation" von Christophe Garban, Gabor Pete und Oded Schramm, arXiv:1008.1378, 2010, vorgestellt. Sie definieren ein Maß, das pivotale Punkte kritischer Perkolation zählt und zeigen, dass es im Limes Gitterweite gegen Null gegen ein Maß konvergiert, das aus der kritischen Perkolation konstruiert werden kann. Dies ist ein wesentlicher Schritt für den Beweis, dass nahkritische Skalenlimiten existieren.

- Monday, 16.5.2011, 16:15, Room MI 03.10.011 at TUM

Mihyun Kang:*Phase transitions in random graphs*

**Abstract:**The phase transition deals with sudden global changes and is observed in many fundamental problems from statistical physics, mathematics and theoretical computer science, for example, Potts models, graph colourings and random k-SAT. The phase transition in random graphs refers to a phenomenon that there is a critical edge density, to which adding a small amount a drastic change in the size of the largest component occurs. In Erdös-Renyi random graph, which begins with an empty graph on n vertices and edges are added randomly one at a time to a graph, a phase transition takes place when the number of edges reaches n/2 and a giant component emerges. Since this seminal work of Erdös and Renyi, various random graph models have been introduced and studied. In this talk we discuss phase transitions in several random graph models, including Erdös-Renyi random graph, random graphs with a given degree sequence, random graph processes and random planar graphs.

- Monday, 6.6.2011, 16:15, Room MI 03.10.011 at TUM

Sebastian Müller (Marseille):*Branching random walks on groups*

**Abstract:**The theory of branching random walks (BRW) on groups is still maiden-like. We survey basic and recent results on BRW and propose some accessible open problems.

A BRW is a system of particles evolving as follows. The process starts with one particle in the group origin. Then at each (discrete) time step a particle branches according to some offspring distribution (with mean m) and moves one step according to an underlying random walk. A BRW is called recurrent if the origin is visited by infinitely many particles with positive probability and transient otherwise. As a consequence of Kesten's amenability criterion any BRW with m>1 is recurrent. There is a phase transition for BRW on non-amenable groups, i.e., there exists some m_c>1 such a BRW with m>m_c is recurrent and with m<m_c></m_c> The talk does not require any specific knowledge on group theory nor on probability theory and is designed for a wider audience.

- Wednesday, 29.6.2011 at 17:15 in Room PR 2.01.11 in Garching-Hochbrück

Peter Mörters :*The giant component in preferential attachment networks*

**Abstract:**We study a dynamical random network model in which at every construction step a new vertex is introduced and attached to every existing vertex independently with a probability proportional to a concave function of its current degree. We use approximation by branching random walks to find necessary and sufficient criteria for the existence and robustness of a giant component in these networks.

The talk is based on joint work with Steffen Dereich (Marburg).

- 10. Erlanger-Münchner Tag der Stochastik on Friday, July 1, 2011

- Monday, 11.7.2011, 16:15, Room MI 03.10.011 at TUM

Janos Engländer (University of Colorado):*Some challenging open problems for spatial branching models*

**Abstract:**I will review some spatial branching models in random environments and with interactions and suggest some (hopefully) interesting open problems. The random environment model is joint work with N. Sieben who provided the simulations.

- Workshop Women in probability July 15-16, 2011

- Monday, 18.7.2011, 16:15.

Andrea Collevecchio

- Monday, 25.7.2011, 16:15.

Noam Berger (Berlin and Jerusalem)