Colloquium Mathematics - Dr. E. Baur

Title: Some aspects of random graphs, random walks in random environment, and random planar maps.

Abstract:

I will give an overview over my research in the last years. In the area of random graphs, I studied mostly in collaboration with Jean Bertoin percolation on families of random increasing trees. Quite recently, an interesting connection between the percolation clusters and random walks with memory was observed, leading to new insights on the latter.

In a different direction, I worked on random walks in random environment which are a small perturbation of the simple symmetric random walk. I will briefly explain some results I obtained in collaboration with Erwin Bolthausen on the exit measures of such walks.

Finally, in the area of random planar maps, I will report on a joint project with Grégory Miermont and Gourab Ray, where we investigated all possible non-compact scaling limits of random quadrangulations with a boundary on the two-sphere.

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