Theoretical Statistics and Mathematics Unit, ISI Delhi

July 27, 2016 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Kumarjit Saha,
TIFR Centre for Applicable Mathematics, Bangalore

Title:
Continuum random tree as scaling limit for drainage network models

Abstract of Talk

People are interested about finding scaling limits of discrete random trees conditioned to be large. Most notably in the case of a Galton-Watson tree with a finite variance critical offspring distribution and conditioned to have a large number of vertices, Aldous [93] proved that the scaling limit is a continuous random tree called the Brownian CRT.
For Scheidegger model of river network the cluster at the origin gives a rooted finite tree with root at the origin and each edge having weight 1 (which is essentially the time distance covered by each edge). Aldous [93] conjectured that such a tree (conditioned to be large) with scaling factor $1/n$ should scale to a continuum random tree like object. We prove that Aldous conjecture is true with a slightly modified scaling limit than what Aldous initially guessed. Our result is a universality class type of result in the sense that the same limit should hold for other drainage network models also in the basin of attraction of the Brownian web.