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Longest Increasing Subsequence under Area Constraint

Mathematical Physics & Probability

Speaker: Riddhi Basu, Stanford University
Related Webpage: https://web.stanford.edu/~rbasu/
Location: 2112 MSB
Start time: Wed, May 24 2017, 4:10PM

Motivated by extremal isoperimetric problems in percolation, I shall describe a

model which puts a global curvature constraint on the classical 
Ulam's problem in the plane, and studies the longest increasing path
from (0,0) to (n,n) trapping atypically large area. As is typical in these
models, the first order behaviour of this random contour is determined by a
variational problem which we explicitly solve. More interesting are exponents
related to local fluctuation properties which capture the competition between the
global curvature constraint and the behaviour of an unconstrained path governed
by KPZ universality. These can be studied via maximal facet lengths of the convex
hull of the contour and the Hausdorff distance from the hull for which we identify
scaling exponents 3/4 and 1/2 respectively. I shall also discuss connections
to different models and several open problems.

Joint work with Shirshendu Ganguly and Alan Hammond.