scholarly journals Rayleigh Random Flights on the Poisson line SIRSN

2020 ◽  
Vol 25 (0) ◽  
Author(s):  
Wilfrid S. Kendall
Keyword(s):  
Random Flights

Random flights on regular graphs

1984 ◽  
Vol 16 (03) ◽  
pp. 618-637 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Automorphism Group ◽  
Transition Probabilities ◽  
Finite Graph ◽  
Initial Position ◽  
Regular Graphs ◽  
Random Flights ◽  
The Past ◽  
Initial Location ◽  
Vertex Set

Let K be a finite graph with vertex set V = {x 0, x 1, …, xσ –1} and automorphism group G. It is assumed that G acts transitively on V. We can imagine that the vertices of K represent σ cities and a traveler visits the cities in a series of random flights. The traveler starts at a given city and in each flight, independently of the past journey, chooses a city at random as the destination. Denote by vn (n = 1, 2, …) the location of the traveler at the end of the nth flight, and by v 0 the initial location. It is assumed that the transition probabilities P{vn = xj | vn –1 = xi }, xi ϵ V, xj ϵ V, do not depend on n and are invariant under the action of G on V. The main result of this paper consists in determining p(n), the probability that the traveler returns to the initial position at the end of the nth flight.

Random Flights in Higher Spaces

2007 ◽  
Vol 20 (4) ◽  
pp. 769-806 ◽  
Author(s):  
E. Orsingher ◽  
A. De Gregorio
Keyword(s):  
Random Flights

Markov Random Flights

2021 ◽  
Author(s):  
Alexander D. Kolesnik
Keyword(s):  
Random Flights ◽  
Markov Random

Ballistic and diffusive random walks in confinement

2005 ◽  
Vol 899 ◽  
Author(s):  
Pierre Levitz ◽  
D. Grebenkov ◽  
D. Petit ◽  
C. Vigouroux
Keyword(s):  
Porous Materials ◽  
Biological Fluids ◽  
Exit Time ◽  
Colloidal Suspensions ◽  
First Exit Time ◽  
Heterogeneous Catalytic ◽  
Random Flights ◽  
Brownian Particles ◽  
Interfacial Confinement ◽  
Random Flight

AbstractPorous materials, concentrated colloidal suspensions are example of confining systems developing large specific surface and presenting a rich variety of shapes. Such an interfacial confinement strongly influences the molecular dynamics of embedded fluids and the diffusive motion of entrapped Brownian particles. An individual trajectory near the interface can be described as an alternate succession of adsorption steps and random flights in the bulk. Statistical properties of these random flights in various interfacial confining systems are determinant to understand the full transport process. Related to first passage processes, these properties play a central role in numerous problems such as the mean first exit time in a bounded domain, heterogeneous catalytic reactivity and nuclear magnetic relaxation in complex and biological fluids. In the present work, we first consider the various possibilities to connect two points of a smooth interface by a random flight in the bulk. Second, we analyze at the theoretical and experimental points of view a way to probe Brownian flights statistics. Implications concerning diffusive transport in disordered porous materials are discussed.

Superposition of the radiation from N independent sources and the problem of random flights

1977 ◽  
Vol 45 (10) ◽  
pp. 964-969 ◽  
Author(s):  
E. Merzbacher ◽  
J. M. Feagin ◽  
T‐H. Wu
Keyword(s):  
Random Flights
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