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Mathematical Physics Seminar

Coalescence on the real line

Bhargav Narayanan- Rutgers University

Location:  Hill 705
Date & time: Thursday, 15 November 2018 at 12:00PM - 1:00PM

Abstract:  Given two probability distributions R and B on the positive reals, colour the real line alternately with red and blue intervals so that the lengths of the red intervals have distribution R, the lengths of the blue intervals have distribution B, and distinct intervals have independent lengths. Now, iteratively update this colouring of the line by coalescing intervals: change the colour of any interval that is surrounded by longer intervals so that these three consecutive intervals subsequently form a single monochromatic interval. Say that a colour (either red or blue) 'wins' if every point of the line is eventually of that colour. I will attempt to answer the following innocuous question: under what conditions is one of the colours a.s. guaranteed to win?

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