Student Seminar
        Continuum Limits of Discrete Random Objects

                                            Summer semester 2019

Donsker’s theorem is a benchmark result in the theory of stochastic processes: discrete-time random walk, with time and space properly rescaled, converges to a continuum object: the Brownian motion. We say that Brownian motion is the scaling limit of simple random walk, and it is indeed the scaling limit of many other random processes with weak dependencies and second spatial moments.

During the seminar, we are focusing on other examples of such scaling limits. A central object with be the continuum random tree, who was first described in seminal work by Aldous (1993). This continuum random tree arises as the scaling limit of random trees and branching processes. We further discuss the scaling limit of critical Erdös-Rényi random graphs.

Target group: Master students in Mathematics, TMP, Finance- and Insurancemathematics
Bachelor students with strong background in Probability Theory and keen interest in the topic may apply for admission.

Prerequisites: Stochastic Processes and/or Discrete Probability

Time:  Fridays 13 - 17 s.t. (biweekly) in room B 251.

Lecturer: Markus Heydenreich

Registration: Please register by email to the lecturer.

Date	Topic
April 26	First meeting, introduction to the topic, distribution of tasks
May 17	The continuum random tree and its properties (N.B.)
May 31	Workshop at TUM
June 14	CRT via fixed points (B.P.)
June 28	Critical Erdös-Rényi random graphs with martingales (V.G.)
July 12	Continuum limits of critical Erdös-Rényi random graphs (D.G.)
July 19	Schaeffer bijection and uniform infinite quadrangulations (D.W. and D.N.)