Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, February 21, 2013, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Johannes Lengler

Drift Analysis - with applications to Yet Another Random Decline

Start with some integer X0. Then iteratively choose the integer Xn+1 uniformly at random between 1 and 1.99*Xn. How long do you need until you reach 1?

For this question we must relate two different concepts. On the one hand, we do know something about the expectation of Xn, or more precisely, about the expected drift Xn-Xn+1. On the other hand, we would like to know something about the hitting time, i.e. the time until we reach 1. Although these are very different concept , they are related by drift analysis. I will show you the basic theorems and how to apply them to random walks.

P.S.: (At least) one result will surprise you.

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