scholarly journals Subsequential scaling limits of simple random walk on the two-dimensional uniform spanning tree

2017 ◽  
Vol 45 (1) ◽  
pp. 4-55 ◽  
Author(s):  
M. T. Barlow ◽  
D. A. Croydon ◽  
T. Kumagai
Keyword(s):  
Random Walk ◽  
Spanning Tree ◽  
Simple Random Walk ◽  
Scaling Limits ◽  
Two Dimensional ◽  
Uniform Spanning Tree

scholarly journals Scaling limits of the three-dimensional uniform spanning tree and associated random walk

2021 ◽  
Vol 49 (6) ◽  
Author(s):  
O. Angel ◽  
D. A. Croydon ◽  
S. Hernandez-Torres ◽  
D. Shiraishi
Keyword(s):  
Random Walk ◽  
Spanning Tree ◽  
Three Dimensional ◽  
Scaling Limits ◽  
Uniform Spanning Tree

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.

The transient behaviour of the simple random walk in the plane

1988 ◽  
Vol 25 (1) ◽  
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.

scholarly journals On the range of a two-dimensional conditioned simple random walk

2019 ◽  
Vol 2 ◽  
pp. 349-368 ◽  
Author(s):  
Nina Gantert ◽  
Serguei Popov ◽  
Marina Vachkovskaia
Keyword(s):  
Random Walk ◽  
Simple Random Walk ◽  
Two Dimensional
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