Minimum Action Curves in Degenerate Finsler Metrics: Existence and Properties: 2134 (Lecture Notes in Mathematics, 2134) - Softcover

Heymann, Matthias

 
9783319177526: Minimum Action Curves in Degenerate Finsler Metrics: Existence and Properties: 2134 (Lecture Notes in Mathematics, 2134)
Softcover
ISBN 10: 3319177524 ISBN 13: 9783319177526
Publisher: Springer, 2015

Synopsis

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.

"synopsis" may belong to another edition of this title.

From the Back Cover

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.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2015
Language
English
ISBN 10 
3319177524
ISBN 13 
9783319177526
Binding
Paperback
Edition number
1
Number of pages
201