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Lecture Notes in Mathematics

Minimum Action Curves in Degenerate Finsler Metrics

Existence and Properties

Authors: Heymann, Matthias

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  • Explores the non-standard geometric view of the Wentzell-Freidlin theory of rare transition events
  • The general geometric framework may spawn applications outside of probability theory
  • Key results and their explanations are well-separated from the necessary technical proofs, making it easy to quickly use the proven existence criteria in practice
  • Includes many intuitive examples with color illustrations
  • Only a knowledge of graduate level analysis is required; all non-standard concepts are introduced as needed
  • Provides detailed complete proofs that do not require any additional work by the reader to fill the gaps
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eBook $39.99
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  • ISBN 978-3-319-17753-3
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Softcover $49.99
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  • ISBN 978-3-319-17752-6
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About this book

Presenting a study of geometric action functionals (i.e., non-negative functionals on the space of unparameterized oriented rectifiable curves), this monograph focuses on the subclass of those functionals whose local action is a degenerate type of Finsler metric that may vanish in certain directions, allowing for curves with positive Euclidean length but with zero action. For such functionals, criteria are developed under which there exists a minimum action curve leading from one given set to another. Then the properties of this curve are studied, and the non-existence of minimizers is established in some settings.

Applied to a geometric reformulation of the quasipotential of Wentzell-Freidlin theory (a subfield of large deviation theory), these results can yield the existence and properties of maximum likelihood transition curves between two metastable states in a stochastic process with small noise.

The book assumes only standard knowledge in graduate-level analysis; all higher-level mathematical concepts are introduced along the way.

 

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-17753-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-319-17752-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.

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Bibliographic Information

Bibliographic Information
Book Title
Minimum Action Curves in Degenerate Finsler Metrics
Book Subtitle
Existence and Properties
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2134
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-17753-3
DOI
10.1007/978-3-319-17753-3
Softcover ISBN
978-3-319-17752-6
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XV, 186
Number of Illustrations
3 b/w illustrations, 11 illustrations in colour
Topics