Correlations of Busemann functions and the 2nd KPZ relationship

Arjun Krishnan (Rochester)

15-Oct-2021, 16:30-17:30 (2 years ago)

Abstract: Busemann functions (correctors in homogenization theory) are objects of interest in first- and last-passage percolation. Determining the correlations of Busemann function increments is important because of its relationship to the second KPZ relationship that relates the two fluctuation exponents in the models. We show that the correlations of adjacent Busemann increments in last-passage percolation with general weights are directly related to the time-constant of last-passage percolation with exponential weights (an integrable model). Using this relationship, we give an easily checkable condition that determines when adjacent Busemann increments are negatively correlated, and prove that, for example, last-passage percolation with iid Bernoulli weights has negatively correlated adjacent Busemann increments.

Joint work with I. Alevy

mathematical physicsprobability

Audience: researchers in the topic


Probability and the City Seminar

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