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Snapshots on quantum probability
Full text linkAs suggested by the title, the goal of the present talk is to describe
some casual photographs of different parts of quantum probability
without pretense of completeness. I will choose three topics which, in
my opinion, efficiently illustrate the fruitful interplay between mathematics
and physics which has characterized the development of quantum
probability in the past thirty years: (i) the description of a recent
experiment which has brought to a conclusion the long standing debate
about possible non local effects as necessary consequences of the
basic principles of quantum mechanics; (ii) the notion of interacting
Fock space, which emerged from quantum electrodynamics without
dipole approximation and turned out to be a fruitful tool in such disparate
fields as orthogonal polynomials, asymptotics of graphs, quantum
structure of classical probability measures, exclusion statistics, . . .
; (iii) the square (and higher powers) of white noise and its relation
to renormalization theory and infinitely divisible processes
On the connection between the probabilistic and the Hilbert space description of a dynamical system
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Classification of probability measures in terms of canonically associated commutation relations
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