Abstract
We consider directed weighted graphs and define various families of path counting functions. Our main results are explicit formulas for the main term of the asymptotic growth rate of these counting functions, under some irrationality assumptions on the lengths of all closed orbits on the graph. In addition we assign transition probabilities to such graphs and compute statistics of the corresponding random walks. Some examples and applications are reviewed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Additional information
To the memory of Boris Pavlov, a teacher, colleague and friend
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Kiro, A., Smilansky, Y., Smilansky, U. (2020). The Distribution of Path Lengths On Directed Weighted Graphs. In: Kurasov, P., Laptev, A., Naboko, S., Simon, B. (eds) Analysis as a Tool in Mathematical Physics. Operator Theory: Advances and Applications, vol 276. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-31531-3_20
Download citation
DOI: https://doi.org/10.1007/978-3-030-31531-3_20
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-31530-6
Online ISBN: 978-3-030-31531-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)