Recurrence of two-dimensional queueing processes, and random walk exit times from the quadrant

2021 ◽  
Vol 31 (6) ◽  
Author(s):  
Marc Peigné ◽  
Wolfgang Woess
Keyword(s):  
Random Walk ◽  
Two Dimensional ◽  
Exit Times ◽  
Queueing Processes

A non-Wiener random walk in a two-dimensional Bernoulli environment

1988 ◽  
Vol 50 (3-4) ◽  
pp. 599-609
Author(s):  
A. Kr�mli ◽  
P. Luk�cs ◽  
D. Sz�sz
Keyword(s):  
Random Walk ◽  
Two Dimensional

scholarly journals Quantum walks and elliptic integrals

2010 ◽  
Vol 20 (6) ◽  
pp. 1091-1098 ◽  
Author(s):  
NORIO KONNO
Keyword(s):  
Random Walk ◽  
Generating Function ◽  
Elliptic Integral ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Elliptic Integrals ◽  
Two Dimensional ◽  
One Dimensional ◽  
Similar Expression ◽  
Return Probability

Pólya showed in his 1921 paper that the generating function of the return probability for a two-dimensional random walk can be written in terms of an elliptic integral. In this paper we present a similar expression for a one-dimensional quantum walk.

scholarly journals Two-dimensional Quantum Random Walk

2010 ◽  
Vol 142 (1) ◽  
pp. 78-107 ◽  
Author(s):  
Yuliy Baryshnikov ◽  
Wil Brady ◽  
Andrew Bressler ◽  
Robin Pemantle
Keyword(s):  
Random Walk ◽  
Two Dimensional ◽  
Quantum Random Walk

Magnetic Breakdown in a dislocated lattice

1965 ◽  
Vol 287 (1409) ◽  
pp. 165-182 ◽  
Keyword(s):  
Electrical Conductivity ◽  
Random Walk ◽  
Dislocation Density ◽  
Network Model ◽  
Random Phase ◽  
Two Dimensional ◽  
Magnetic Breakdown ◽  
Low Dislocation Density ◽  
Electron Orbit ◽  
Straight Lines

The network model of electron orbits coupled by magnetic breakdown is extended to a two dimensional metal containing dislocations. It is shown that the network is still likely to be a valid representation, but the phase lengths of the arms are altered, and a very low dislocation density (about one per electron orbit) is enough to produce almost complete randomization. The Bloch-like quasi-particles that can travel in straight lines on a perfect network are now heavily scattered, and it is preferable to think of electrons performing a random walk on the arms of the network, although the justification for this procedure is somewhat doubtful. A simpler alternative to Falicov & Sievert’s method is presented for calculating the electrical conductivity of a random-phase network, and is extended to cases where randomness affects only some of the phases, as is believed to be the situation in real metals like zinc and magnesium.

A two-dimensional random walk in the presence of a partially reflecting barrier

1974 ◽  
Vol 11 (01) ◽  
pp. 199-205
Author(s):  
Noel Cressie
Keyword(s):  
Random Walk ◽  
Two Dimensional ◽  
Absorption Probabilities

A general two-dimensional random walk is considered with a barrier along the y-axis. Absorption probabilities are derived when the barrier is absorbing, and when it is semi-reflecting.

The transient behaviour of the simple random walk in the plane

1988 ◽  
Vol 25 (01) ◽  
pp. 58-69 ◽  
Author(s):  
D. Y. Downham ◽  
S. B. Fotopoulos
Keyword(s):  
Random Walk ◽  
Transient Process ◽  
Asymptotic Form ◽  
Simple Random Walk ◽  
Rectangular Lattice ◽  
Two Dimensional ◽  
Transient Behaviour ◽  
Practical Implications ◽  
Asymptotic Forms

For the simple two-dimensional random walk on the vertices of a rectangular lattice, the asymptotic forms of several properties are well known, but their forms can be insufficiently accurate to describe the transient process. Inequalities with the correct asymptotic form are derived for six such properties. The rates of approach to the asymptotic form are derived. The accuracy of the bounds and some practical implications of the results are discussed.

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