Events


Bauingenieurgebäude

 

  • Research Seminar (Thursdays)

    17 May 2018: Dr. Alexander MarynychWeak convergence of random polytopes: the continous mapping approach
    24 May 2018: Jan-Erik LübbersDisplacement of biased random walk in a one-dimensional percolation model
    21 June 2018: Dr. Christian Mönch - Large deviations and distances in the spatial preferential attachment model


  • Innsbruck-München-Kolloquium* (Friday, 20 April 2018)

    Prof. Dr. Noam BergerAggregation processes in the half plane
    Univ. Prof. Dr. Thomas FranoschExact Nonlinear Response Theory in the Driven Lattice Lorentz Gas
    Dr. Jan NagelEinstein relation and steady states for the random conductance model

 

 

TITLE Weak convergence of random polytopes: the continous mapping approach
SPEAKER Dr. Alexander Marynych (Kyiv)
TIME Thursday, 17 May 2018, 4:15 pm
LOCATION Campus Technik, Seminarraum 734 (Mathematik)
ABSTRACT In my talk I will discuss how the celebrated continuous mapping theorem can be applied to derive weak limit theorems for random polytopes and their various characteristics. A special emphasis will be placed on recent results about weak convergence of random cones obtained in a joint work with Z. Kabluchko (Münster), C. Thäle and D. Temesvari (Bochum).



TITLE Displacement of biased random walk in a one-dimensional percolation model
SPEAKER Jan-Erik Lübbers (TU Darmstadt)
TIME Thursday, 24 May 2018, 4:15 pm
LOCATION Campus Technik, Seminarraum 734 (Mathematik)
ABSTRACT Suppose an ant is placed in a randomly generated, infinite maze. Having no orientation whatsoever, it starts to move along according to a nearest neighbour random walk. Now furthermore, suppose the maze is tilted, such that the ant makes a step along the slope with higher probability than in the opposite direction. Tracking the ant's position, we are interested in the long-term behaviour of the corresponding random walk.

We study this model in the context that the maze is given by a one-dimensional percolation cluster. Depending on the bias of the walk, its linear speed converges almost surely towards a deterministic value. This limit exhibits a phase transition from positive value to zero at a critical value of the bias. We investigate the typical order of fluctuations of the walk in the ballistic speed regime, and the order of displacement from the origin in the subballistic speed regime.


TITLE Large deviations and distances in the spatial preferential attachment model
SPEAKER Dr. Christian Mönch (Universität Mannheim)
TIME Thursday, 21 June 2018, 4:15 pm
LOCATION Campus Technik, Seminarraum Mathematik 734 (Mathematik)
ABSTRACT Pferential attachment models are self-reinforced growth models for complex networks. Recently, there has been much interest in developing PA models for networks embeded into some underlying geometric space. For one such model, proposed by Jacob and Mörters, I will discuss a Large Deviation principle for empirical vertex neighbourhoods and the asymptotics of the distance of two typical vertices in the giant component. The talk is based on joint work with Christian Hirsch (Aalborg).                                                    



TITLE Aggregation processes in the half plane
SPEAKER Prof. Dr. Noam Berger (TU München)
TIME Friday, 20 April 2018, 1:15 pm - 2:15 pm
LOCATION Campus Technik, HSB4
ABSTRACT We discuss both the DLA and the Hastings Levitov process on the half plane, where the seed of growth is the entire real line. It turns out that these processes behave very differently from their whole plane counterparts. We show a few results and present several conjectures. Based on joint work with J. Kagan, E. Procaccia and A. Turner.


TITLE Exact Nonlinear Response Theory in the Driven Lattice Lorentz Gas
SPEAKER Univ.-Prof. Dr. Thomas Franosch (Universität Innsbruck)
TIME Friday, 20 April 2018, 2:30 pm - 3:30 pm
LOCATION Campus Technik, HSB4
ABSTRACT pdf                                                                                                                                                                                           


TITLE Einstein relation and steady states for the random conductance model
SPEAKER Dr. Jan Nagel (TU Eindhoven)
TIME Friday, 20 April 2018, 4:00 pm - 5:00 pm
LOCATION Campus Technik, HSB4
ABSTRACT The Einstein relation says that for a motion under external force the derivative of the effective velocity at 0 (as a function of the strength of the force) is given by the diffusivity of the unperturbed motion.

We prove the Einstein relation for the random walk in Z^d, when the transition probabilities are determined by random conductances of the edges, chosen independently and identically distributed and bounded away from 0 and infinity. We also relate it to an expansion of the steady state, the stationary measure for the environment seen from the random walker.

The proof is based on Lebowitz and Rost's argument using Girsanov's theorem to obtain an alternative description of the diffusivity and a regeneration structure for the biased process, which is robust for small values of the bias. The talk is based on a joint work with Nina Gantert and Xiaoqin Guo.


* There is no conference fee for this event and everybody interested is invited to attend.