# Noon lecture

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On 6.12.2016 at 14:00 in S1, there is the following noon lecture:

# The phase transition in the random d-process

## Lutz Warnke

## University of Cambridge and Georgia Institute of Technology

## Abstract

(based on joint work with Nick Wormald)

One of the most interesting features of Erdős-Rényi random graphs is the "percolation phase transition", where the global structure intuitively changes from only small components to a single giant component plus small ones. In this talk we discuss the percolation phase transition in the random d-process, which corresponds to a natural algorithmic model for generating random regular graphs that differs from the usual configuration model (starting with an empty graph on n vertices, the random d-process evolves by sequentially adding new random edges so that the maximum degree remains at most d). Our results on the phase transition solve a problem of Wormald from 1997, and verify a conjecture of Balińska and Quintas from 1990.

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