Correlations of Busemann functions and the 2nd KPZ relationship
Busemann functions are objects of interest in first- and last-passage percolation. Determining the correlations of Busemann function increments is important because of their relationship to the second KPZ relationship that relates the two fluctuation exponents in the model. We show that the correlations of adjacent Busemann increments in last-passage percolation with general weights are, in fact, directly related to the time-constant of last-passage percolation with exponential weights (a well-known integrable model). Using this relationship, we give an easily checkable condition that determines when adjacent Busemann increments are negatively correlated.
Joint work with I. Alevy