We give an approach to large deviation type asymptotic problems without evident probabilistic representation behind. An example provided by the mean field models of quantum statistical mechanics is considered.
In this work we consider non-relativistic quantum mechanics, obtained from a classical configuration space of indistinguishable particles. Following an approach proposed in [8], wave functions are regarded as elements of suitable projective modules over . We take furthermore into account the -Theory point of view (cf. [HPRS,S]) where the role of group action is particularly emphasized. As an example illustrating the method, the case of two particles is worked out in detail. Previous works (cf....
We survey some of the universality properties of the Riemann zeta function and then explain how to obtain a natural quantization of Voronin’s universality theorem (and of its various extensions). Our work builds on the theory of complex fractal dimensions for fractal strings developed by the second author and M. van Frankenhuijsen in [60]. It also makes an essential use of the functional analytic framework developed by the authors in [25] for rigorously studying the spectral operator (mapping...
In 1992, Speicher showed the fundamental fact that the probability measures playing the role of the classical Gaussian in the various non-commutative probability theories (viz. fermionic probability, Voiculescu’s free probability, and -deformed probability of Bożejko and Speicher) all arise as the limits in a generalized Central Limit Theorem. The latter concerns sequences of non-commutative random variables (elements of a -algebra equipped with a state) drawn from an ensemble of pair-wise commuting...