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The seminar on Stochastic Analysis and Mathematical Physics of the
Ca tholic University of Chile, started in Santiago in 1984, has
being followed and enlarged since 1995 by a series of international
workshops aimed at pro moting a wide-spectrum dialogue between
experts on the fields of classical and quantum stochastic analysis,
mathematical physics, and physics. This volume collects most of the
contributions to the Fourth Interna tional Workshop on Stochastic
Analysis and Mathematical Physics (whose Spanish abbreviation is
"ANESTOC"; in English, "STAMP"), held in San tiago, Chile, from
January 5 to 11, 2000. The workshop style stimulated a vivid
exchange of ideas which finally led to a number of written con
tributions which I am glad to introduce here. However, we are
currently submitted to a sort of invasion of proceedings books, and
we do not want to increase our own shelves with a new one of the
like. On the other hand, the editors of conference proceedings have
to use different exhausting and com pulsive strategies to persuade
authors to write and provide texts in time, a task which terrifies
us. As a result, this volume is aimed at smoothly start ing a new
kind of publication. What we would like to have is a collection of
books organized like our seminar.
This volume contains current work at the frontiers of research in
quantum probability, infinite dimensional stochastic analysis,
quantum information and statistics. It presents a carefully chosen
collection of articles by experts to highlight the latest
developments in those fields. Included in this volume are
expository papers which will help increase communication between
researchers working in these areas. The tools and techniques
presented here will be of great value to research mathematicians,
graduate students and applied mathematicians.
The seminar on Stochastic Analysis and Mathematical Physics started
in 1984 at the Catholic University of Chile in Santiago and has
been an on going research activity. Since 1995, the group has
organized international workshops as a way of promoting a broader
dialogue among experts in the areas of classical and quantum
stochastic analysis, mathematical physics and physics. This volume,
consisting primarily of contributions to the Third Inter national
Workshop on Stochastic Analysis and Mathematical Physics (in
Spanish ANESTOC), held in Santiago, Chile, in October 1998, focuses
on an analysis of quantum dynamics and related problems in
probability the ory. Various articles investigate quantum dynamical
semigroups and new results on q-deformed oscillator algebras, while
others examine the appli cation of classical stochastic processes
in quantum modeling. As in previous workshops, the topic of quantum
flows and semigroups occupied an important place. In her paper, R.
Carbone uses a spectral type analysis to obtain exponential rates
of convergence towards the equilibrium of a quantum dynamical
semigroup in the GBP2 sense. The method is illus trated with a
quantum extension of a classical birth and death process. Quantum
extensions of classical Markov processes lead to subtle problems of
domains. This is in particular illustrated by F. Fagnola, who
presents a pathological example of a semigroup for which the
largest * -subalgebra (of the von Neumann algebra of bounded linear
operators of GBP2 (lR+, IC)), con tained in the domain of its
infinitesimal generator, is not a-weakly dense.
The seminar on Stochastic Analysis and Mathematical Physics started
in 1984 at the Catholic University of Chile in Santiago and has
been an on going research activity. Since 1995, the group has
organized international workshops as a way of promoting a broader
dialogue among experts in the areas of classical and quantum
stochastic analysis, mathematical physics and physics. This volume,
consisting primarily of contributions to the Third Inter national
Workshop on Stochastic Analysis and Mathematical Physics (in
Spanish ANESTOC), held in Santiago, Chile, in October 1998, focuses
on an analysis of quantum dynamics and related problems in
probability the ory. Various articles investigate quantum dynamical
semigroups and new results on q-deformed oscillator algebras, while
others examine the appli cation of classical stochastic processes
in quantum modeling. As in previous workshops, the topic of quantum
flows and semigroups occupied an important place. In her paper, R.
Carbone uses a spectral type analysis to obtain exponential rates
of convergence towards the equilibrium of a quantum dynamical
semigroup in the GBP2 sense. The method is illus trated with a
quantum extension of a classical birth and death process. Quantum
extensions of classical Markov processes lead to subtle problems of
domains. This is in particular illustrated by F. Fagnola, who
presents a pathological example of a semigroup for which the
largest * -subalgebra (of the von Neumann algebra of bounded linear
operators of GBP2 (lR+, IC)), con tained in the domain of its
infinitesimal generator, is not a-weakly dense.
The seminar on Stochastic Analysis and Mathematical Physics of the
Ca tholic University of Chile, started in Santiago in 1984, has
being followed and enlarged since 1995 by a series of international
workshops aimed at pro moting a wide-spectrum dialogue between
experts on the fields of classical and quantum stochastic analysis,
mathematical physics, and physics. This volume collects most of the
contributions to the Fourth Interna tional Workshop on Stochastic
Analysis and Mathematical Physics (whose Spanish abbreviation is
"ANESTOC"; in English, "STAMP"), held in San tiago, Chile, from
January 5 to 11, 2000. The workshop style stimulated a vivid
exchange of ideas which finally led to a number of written con
tributions which I am glad to introduce here. However, we are
currently submitted to a sort of invasion of proceedings books, and
we do not want to increase our own shelves with a new one of the
like. On the other hand, the editors of conference proceedings have
to use different exhausting and com pulsive strategies to persuade
authors to write and provide texts in time, a task which terrifies
us. As a result, this volume is aimed at smoothly start ing a new
kind of publication. What we would like to have is a collection of
books organized like our seminar."
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