Probability seminar: Palm Theory and Shift-Coupling

6 May 2016, 3.40 PM - 6 May 2016, 4.40 PM

Hermann Thorisson, University of Iceland

SM3, School of Mathematics

Hermann Thorisson, University of Iceland

Palm Theory and Shift-Coupling

Palm versions w.r.t. stationary random measures are mass-stationary, that is, the origin is at a typical location in the mass of the random measure. For a simple example, consider the stationary Poisson process on the line conditioned on having a point at the origin. The origin is then at a typical point (at a typical location in the mass) because shifting the origin to the nth point on the right (or on the left) does not alter the fact that the inter-point distances are i.i.d. exponential. Another (less obvious) example is the local time at zero of a two-sided standard Brownian motion.

In this talk we shall first consider mass-stationarity on the line and the shift-coupling problem of how to shift the origin from a typical location in the mass of one random measure to a typical location in the mass of another random measure. Applications include finding patterns like the Brownian bridge in the realisation of a Brownian motion, and also patterns in planar Brownian motion. If time allows we shall then extend the view beyond the line, moving through the Poisson process in the plane and d-dimensional space towards general random measures on groups.

Contact information

Organisers: Marton Balazs, Haeran Cho

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