### Order of fluctuations for the discrete Hammersley process.

Probability Seminar

27th April 2018, 3:30 pm – 4:30 pm

Main Maths Building, SM4

We discuss the order of the variance on a lattice analogue of the Hammersley process, for which the environment on each site has independent, Bernoulli distributed values.

The last passage time is the maximum number of Bernoulli points that can be collected on a piecewise linear path, where each segment has strictly positive but finite slope.

For this model the shape function exhibits two flat edges and we study the order of the variance in directions that fall in the flat edge, in directions that approximate the edge of the flat edge,

and in directions in the strictly concave section of the shape for the i.i.d. model and for the associated equilibrium model with boundaries. This is joint work with Janosch Ortmann and Federico Ciech.

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