Joint BCAM-UPV/EHU Analysis and PDE seminar: Loop measures and isomorphism theorems for space-time random walks

LOCATION: BCAM

Abstract
Loop measures have become important in the analysis of random walks and their applications in mathematical physics and are currently an active field of research. The concepts of measures go back to Symanzik in the late 1960s in the context of Euclidean field theory. We introduce a novel class of such measures - namely loop measures on graphs with countable infinite different time horizons. The loops are generated by space-time random walks where we add dimension - called 'time' - to the integer lattice in $ d $ dimensions, $ dge 3$. These measures are connected to the cycle representation of partition functions in quantum systems (Boson systems). We derive corresponding Dynkin isomorphism theorems for space-time random walks which are complex Gaussian measures, and we show the onset of the so-called Bose-Einstein condensation for some examples.

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