Probability seminar: Longest increasing path within the critical strip

27 May 2016, 3.40 PM - 27 May 2016, 4.40 PM

Mathew Joseph, University of Sheffield

SM3, School of Mathematics

Mathew Joseph, Sheffield

Longest increasing path within the critical strip

Consider the square [0, n]2 with points from a Poisson point process of intensity 1 distributed within it. In a seminal work, Baik, Deift and Johansson proved that the number of points Ln (length) on a maximal increasing path (an increasing path that contains the most number of points), when properly centered and scaled, converges to the Tracy-Widom distribution. Later Johansson showed that all maximal paths lie within the strip of width n2/3+ε around the diagonal with probability tending to 1 as n → ∞. We shall discuss recent work on the Gaussian behaviour of the length Ln(γ) of a maximal increasing path restricted to lie within a strip of width nγ, γ<2/3. This is based on joint work with Partha Dey and Ron Peled.

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Organisers: Marton Balazs, Haeran Cho

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