Minimum Action Curves in Degenerate Finsler Metrics (Paperback)

Matthias Heymann

ISBN 10: 3319177524 / ISBN 13: 9783319177526

Published by Springer International Publishing AG, Cham, 2015

About this Item

Paperback. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9783319177526

Bibliographic Details

• Title: Minimum Action Curves in Degenerate Finsler Metrics (Paperback)
• Publisher: Springer International Publishing AG, Cham
• Publication Date: 2015
• Language: English
• ISBN 10: 3319177524
• ISBN 13: 9783319177526
• Binding: Paperback
• Edition: 1st Edition
• Condition: new

About this title

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.