Fluctuation Theory for the Ehrenfest urn

1991 ◽  
Vol 23 (3) ◽  
pp. 598-611 ◽  
Author(s):  
N. H. Bingham
Keyword(s):  
Random Walk ◽  
Statistical Mechanics ◽  
Continuous Time ◽  
Reliability Theory ◽  
Unit Cube ◽  
Fluctuation Theory ◽  
Urn Model ◽  
First Passage ◽  
Opposite Vertex

The Ehrenfest urn model with d balls, or alternatively random walk on the unit cube in d dimensions, is considered in discrete and continuous time, together with related models. Attention is focused on the fluctuation theory of the model—behaviour on unusual states—and in particular on first passage to the opposite vertex. Applications to statistical mechanics, reliability theory and genetics are surveyed, and some new results are obtained.

Fluctuation Theory for the Ehrenfest urn

1991 ◽  
Vol 23 (03) ◽  
pp. 598-611 ◽  
Author(s):  
N. H. Bingham
Keyword(s):  
Random Walk ◽  
Statistical Mechanics ◽  
Continuous Time ◽  
Reliability Theory ◽  
Unit Cube ◽  
Fluctuation Theory ◽  
Urn Model ◽  
First Passage ◽  
Opposite Vertex

The Ehrenfest urn model withdballs, or alternatively random walk on the unit cube inddimensions, is considered in discrete and continuous time, together with related models. Attention is focused on the fluctuation theory of the model—behaviour on unusual states—and in particular on first passage to the opposite vertex. Applications to statistical mechanics, reliability theory and genetics are surveyed, and some new results are obtained.

scholarly journals Fluctuation theory for the Ehrenfest urn via electric networks

1993 ◽  
Vol 25 (02) ◽  
pp. 472-476 ◽  
Author(s):  
José Luis Palacios
Keyword(s):  
Fluctuation Theory ◽  
Network Approach ◽  
Urn Model ◽  
Electric Networks ◽  
First Passage ◽  
Electric Network ◽  
Opposite Vertex

Using the electric network approach, we give very simple derivations for the expected first passage from the origin to the opposite vertex in the d-cube (i.e. the Ehrenfest urn model) and the Platonic graphs.

scholarly journals Fluctuation theory for the Ehrenfest urn via electric networks

1993 ◽  
Vol 25 (2) ◽  
pp. 472-476 ◽  
Author(s):  
José Luis Palacios
Keyword(s):  
Fluctuation Theory ◽  
Network Approach ◽  
Urn Model ◽  
Electric Networks ◽  
First Passage ◽  
Electric Network ◽  
Opposite Vertex

Using the electric network approach, we give very simple derivations for the expected first passage from the origin to the opposite vertex in thed-cube (i.e. the Ehrenfest urn model) and the Platonic graphs.

Quartile histogram assessment of glioma malignancy using high b ‐value diffusion MRI with a continuous‐time random‐walk model

2021 ◽  
Vol 34 (4) ◽  
Author(s):  
M. Muge Karaman ◽  
Jiaxuan Zhang ◽  
Karen L. Xie ◽  
Wenzhen Zhu ◽  
Xiaohong Joe Zhou
Keyword(s):  
Random Walk ◽  
Continuous Time ◽  
Diffusion Mri ◽  
B Value ◽  
Continuous Time Random Walk ◽  
Random Walk Model ◽  
High B Value

scholarly journals Strong Local Survival of Branching Random Walks is Not Monotone

2014 ◽  
Vol 46 (02) ◽  
pp. 400-421 ◽  
Author(s):  
Daniela Bertacchi ◽  
Fabio Zucca
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Generating Function ◽  
Continuous Time ◽  
Local Property ◽  
Branching Random Walk ◽  
Infinite Dimensional ◽  
Branching Random Walks ◽  
Local Survival ◽  
Branching Law

In this paper we study the strong local survival property for discrete-time and continuous-time branching random walks. We study this property by means of an infinite-dimensional generating functionGand a maximum principle which, we prove, is satisfied by every fixed point ofG. We give results for the existence of a strong local survival regime and we prove that, unlike local and global survival, in continuous time, strong local survival is not a monotone property in the general case (though it is monotone if the branching random walk is quasitransitive). We provide an example of an irreducible branching random walk where the strong local property depends on the starting site of the process. By means of other counterexamples, we show that the existence of a pure global phase is not equivalent to nonamenability of the process, and that even an irreducible branching random walk with the same branching law at each site may exhibit nonstrong local survival. Finally, we show that the generating function of an irreducible branching random walk can have more than two fixed points; this disproves a previously known result.

Multiscale Modeling of Carbonate Acidizing Using Continuous Time Random Walk Approach

2017 ◽  
Author(s):  
Kang Kang ◽  
Elsayed Abdelfatah ◽  
Maysam Pournik ◽  
Bor Jier Shiau ◽  
Jeffrey Harwell
Keyword(s):  
Random Walk ◽  
Multiscale Modeling ◽  
Continuous Time ◽  
Continuous Time Random Walk ◽  
Carbonate Acidizing
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