Random walk of a particle interacting with a random field

1994 ◽  
pp. 77-89
Author(s):  
R. A. Minlos
Keyword(s):  
Random Walk ◽  
Random Field

Random walk in a random environment with correlated sites

2001 ◽  
Vol 38 (4) ◽  
pp. 1018-1032 ◽  
Author(s):  
T. Komorowski ◽  
G. Krupa
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Random Field ◽  
Random Environment ◽  
Law Of Large Numbers ◽  
Transition Probabilities ◽  
Direct Application ◽  
Random Environments ◽  
Large Numbers ◽  
Stationary Random Field

We prove the law of large numbers for random walks in random environments on the d-dimensional integer lattice Zd. The environment is described in terms of a stationary random field of transition probabilities on the lattice, possessing a certain drift property, modeled on the Kalikov condition. In contrast to the previously considered models, we admit possible correlation of transition probabilities at different sites, assuming however that they become independent at finite distances. The possible dependence of sites makes impossible a direct application of the renewal times technique of Sznitman and Zerner.

The multitype branching random walk: temporal and spatial limit theorems

1989 ◽  
Vol 21 (03) ◽  
pp. 491-512
Author(s):  
B. Gail Ivanoff
Keyword(s):  
Random Walk ◽  
Random Field ◽  
Random Fields ◽  
Limit Theorems ◽  
Branching Random Walk ◽  
Initial Field ◽  
Large Numbers ◽  
Poisson Random Fields ◽  
The Mean ◽  
Temporal And Spatial

We consider a multitype branching random walk with independent Poisson random fields of each type of particle initially. The existence of limiting random fields as the generation number, is studied, when the intensity of the initial field is renormalized in such a way that the mean measures converge. Spatial laws of large numbers and central limit theorems are given for the limiting random field, when it is non-trivial.

Random walk in a random environment with correlated sites

2001 ◽  
Vol 38 (04) ◽  
pp. 1018-1032 ◽  
Author(s):  
T. Komorowski ◽  
G. Krupa
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Random Field ◽  
Random Environment ◽  
Law Of Large Numbers ◽  
Transition Probabilities ◽  
Direct Application ◽  
Random Environments ◽  
Large Numbers ◽  
Stationary Random Field

We prove the law of large numbers for random walks in random environments on the d-dimensional integer lattice Z d . The environment is described in terms of a stationary random field of transition probabilities on the lattice, possessing a certain drift property, modeled on the Kalikov condition. In contrast to the previously considered models, we admit possible correlation of transition probabilities at different sites, assuming however that they become independent at finite distances. The possible dependence of sites makes impossible a direct application of the renewal times technique of Sznitman and Zerner.

The multitype branching random walk: temporal and spatial limit theorems

1989 ◽  
Vol 21 (3) ◽  
pp. 491-512 ◽  
Author(s):  
B. Gail Ivanoff
Keyword(s):  
Random Walk ◽  
Random Field ◽  
Random Fields ◽  
Limit Theorems ◽  
Branching Random Walk ◽  
Initial Field ◽  
Large Numbers ◽  
Poisson Random Fields ◽  
The Mean ◽  
Temporal And Spatial

We consider a multitype branching random walk with independent Poisson random fields of each type of particle initially. The existence of limiting random fields as the generation number, is studied, when the intensity of the initial field is renormalized in such a way that the mean measures converge. Spatial laws of large numbers and central limit theorems are given for the limiting random field, when it is non-trivial.

Elements of the Random Walk

2004 ◽  
Author(s):  
Joseph Rudnick ◽  
George Gaspari
Keyword(s):  
Random Walk

Comparison of random field strengths in (1-x)SrTiO3-xBiFeO3 and (1-x)SrTiO3-xBaTiO3 relaxor ferroelectrics by means of acoustic emission

2020 ◽  
Vol 92 (2) ◽  
pp. 20401
Author(s):  
Evgeniy Dul'kin ◽  
Michael Roth
Keyword(s):  
Acoustic Emission ◽  
Random Field ◽  
Electric Fields ◽  
Bias Field ◽  
Relaxor Ferroelectrics ◽  
External Bias ◽  
Field Strengths

In relaxor (1-x)SrTiO3-xBiFeO3 ferroelectrics ceramics (x = 0.2, 0.3 and 0.4) both intermediate temperatures and Burns temperatures were successfully detected and their behavior were investigated in dependence on an external bias field using an acoustic emission. All these temperatures exhibit a non-trivial behavior, i.e. attain the minima at some threshold fields as a bias field enhances. It is established that the threshold fields decrease as x increases in (1-x)SrTiO3-xBiFeO3, as it previously observed in (1-x)SrTiO3-xBaTiO3 (E. Dul'kin, J. Zhai, M. Roth, Phys. Status Solidi B 252, 2079 (2015)). Based on the data of the threshold fields the mechanisms of arising of random electric fields are discussed and their strengths are compared in both these relaxor ferroelectrics.

CUBIC [001] TWIST CSL GRAIN BOUNDARIES STUDY BY MEANS OF RANDOM WALK

1990 ◽  
Vol 51 (C1) ◽  
pp. C1-67-C1-69
Author(s):  
P. ARGYRAKIS ◽  
E. G. DONI ◽  
TH. SARIKOUDIS ◽  
A. HAIRIE ◽  
G. L. BLERIS
Keyword(s):  
Random Walk ◽  
Grain Boundaries
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