BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Arjun Krishnan (Rochester) DTSTART:20211015T163000Z DTEND:20211015T173000Z DTSTAMP:20260423T005652Z UID:PatC/44 DESCRIPTION:Title: Co rrelations of Busemann functions and the 2nd KPZ relationship\nby Arju n Krishnan (Rochester) as part of Probability and the City Seminar\n\n\nAb stract\nBusemann functions (correctors in homogenization theory) are objec ts of interest in first- and last-passage percolation. Determining the cor relations of Busemann function increments is important because of its rela tionship to the second KPZ relationship that relates the two fluctuation e xponents 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 perco lation with iid Bernoulli weights has negatively correlated adjacent Busem ann increments.\n\nJoint work with I. Alevy\n LOCATION:https://researchseminars.org/talk/PatC/44/ END:VEVENT END:VCALENDAR