Stochastic Processes, Physics and Geometry

by Gesztesy, Fritz; Holden, Helge; Jose, Jurgen; Paycha, Sylvie; Rockner, Michael; Scarlatti, Sergio

• ISBN13: 9780821819609
• ISBN10: 0821819607
• Format: Paperback
• Copyright: 2000-09-01
• Publisher: Amer Mathematical Society

Summary

This volume and Stochastic Processes, Physics and Geometry: New Interplays I present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, "Infinite Dimensional (Stochastic) Analysis and Quantum Physics", was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry. The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and noncommutative probability theory, integrable systems, quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas. Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional contributed papers. Members of the Canadian Mathematical Society may order at the AMS member price.

Table of Contents

Preface	ix
A Brief Curriculum Vitae of Sergio Albeverio	1	(2)
Students and postdoctoral fellows supervised	3	(6)
Sergio Albeverio
Publications of Sergio Albeverio	9	(28)
On the occasion of Sergio Albeverio's 60th birthday	37	(4)
Ph. Blanchard
Growth and saturation in random media	41	(14)
G. Ben Arous
A. F. Ramirez
Maximal inequalities and exponential estimates for stochastic convolutions in Banach spaces	55	(10)
Z. Brzezniak
S. Peszat
On Markov evolution equations in quotient probability spaces	65	(20)
A. M. Chebotarev
V. P. Maslov
Maximal dissipativity of the Dirichlet operator corresponding to the Burgers equation	85	(14)
G. Da Prato
A. Debussche
The Schrodinger equation with moving point interactions in three dimensions	99	(16)
G. F. Dell'Antonio
R. Figari
A. Teta
The square of self intersection local time of Brownian motion	115	(8)
C. Drumond
M. de Faria
L. Streit
On the role of flux in scattering theory	123	(16)
D. Durr
S. Teufel
Probability and nonlinear analysis	139	(6)
E. B. Dynkin
Special Ito maps and an L2 Hodge theory for one forms on path spaces	145	(18)
K. D. Elworthy
Xue-Mei Li
The classical massive Thirring system revisited	163	(38)
V. Z. Enolskii
F. Gesztesy
H. Holden
On Ito's formulae for additive functionals of symmetric diffusion processes	201	(12)
M. Fukushima
Spectral theory of sparse potentials	213	(26)
D. Hundertmark
W. Kirsch
Invariant measures under Schrodinger evolution and quantum statistical mechanics	239	(4)
G. Jona-Lasinio
Exponential mixing for classical continuous systems	243	(12)
Yu. G. Kondratiev
R. A. Minlos
M. Rockner
G. V. Shchepan'uk
Diffusions on ``simple'' configuration spaces	255	(16)
Zhi-Ming Ma
M. Rockner
One- and two-particle branches of the spectrum of ``many component'' operators	271	(12)
R. A. Minlos
Representation integrale de fonctionnelles analytiques positives	283	(8)
H. Ouerdiane
A. Rezgui
Mean field models and propagation of chaos in feedforward neural networks	291	(12)
M. Piccioni
S. Scarlatti
Path properties of a class of Gaussian processes with applications to spde's	303	(14)
M. Sanz-Sole
M. Sarra
A Feynman-Kac formula for unbounded semigroups	317	(6)
B. Simon
Hypercontractivity in non-commutative Lp spaces	323
B. Zegarlinski