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

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 X_n+1 uniformly at random between 1 and 1.99*X_n. 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 X_n, or more precisely, about the expected drift X_n-X_n+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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