scholarly journals Quenched and averaged tails of the heat kernel of the two-dimensional uniform spanning tree

2021 ◽  
Author(s):  
M. T. Barlow ◽  
D. A. Croydon ◽  
T. Kumagai
Keyword(s):  
Heat Kernel ◽  
Spanning Tree ◽  
Two Dimensional ◽  
Uniform Spanning Tree

A Constrained Delaunay Triangulation Algorithm Based on Incremental Points

2011 ◽  
Vol 90-93 ◽  
pp. 3277-3282 ◽  
Author(s):  
Bai Chao Wu ◽  
Ai Ping Tang ◽  
Lian Fa Wang
Keyword(s):  
Information System ◽  
Data Structures ◽  
Delaunay Triangulation ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Three Dimensional ◽  
Geographical Information ◽  
Two Dimensional ◽  
Data Set ◽  
Constrained Delaunay Triangulation

The foundation ofdelaunay triangulationandconstrained delaunay triangulationis the basis of three dimensional geographical information system which is one of hot issues of the contemporary era; moreover it is widely applied in finite element methods, terrain modeling and object reconstruction, euclidean minimum spanning tree and other applications. An algorithm for generatingconstrained delaunay triangulationin two dimensional planes is presented. The algorithm permits constrained edges and polygons (possibly with holes) to be specified in the triangulations, and describes some data structures related to constrained edges and polygons. In order to maintain the delaunay criterion largely，some new incremental points are added onto the constrained ones. After the data set is preprocessed, the foundation ofconstrained delaunay triangulationis showed as follows: firstly, the constrained edges and polygons generate initial triangulations，then the remained points completes the triangulation . Some pseudo-codes involved in the algorithm are provided. Finally, some conclusions and further studies are given.

scholarly journals The Local Limit of the Uniform Spanning Tree on Dense Graphs

2018 ◽  
Vol 173 (3-4) ◽  
pp. 502-545
Author(s):  
Jan Hladký ◽  
Asaf Nachmias ◽  
Tuan Tran
Keyword(s):  
Spanning Tree ◽  
Local Limit ◽  
Uniform Spanning Tree ◽  
Dense Graphs

scholarly journals Semi-Infinite Paths of the Two-Dimensional Radial Spanning Tree

2013 ◽  
Vol 45 (4) ◽  
pp. 895-916 ◽  
Author(s):  
François Baccelli ◽  
David Coupier ◽  
Viet Chi Tran
Keyword(s):  
Point Process ◽  
Infinite Number ◽  
Spanning Tree ◽  
Poisson Point Process ◽  
Two Dimensional ◽  
Infinite Path ◽  
Intersection Points

We study semi-infinite paths of the radial spanning tree (RST) of a Poisson point process in the plane. We first show that the expectation of the number of intersection points between semi-infinite paths and the sphere with radius r grows sublinearly with r. Then we prove that in each (deterministic) direction there exists, with probability 1, a unique semi-infinite path, framed by an infinite number of other semi-infinite paths of close asymptotic directions. The set of (random) directions in which there is more than one semi-infinite path is dense in [0, 2π). It corresponds to possible asymptotic directions of competition interfaces. We show that the RST can be decomposed into at most five infinite subtrees directly connected to the root. The interfaces separating these subtrees are studied and simulations are provided.

scholarly journals Heat Kernel Coefficients for Two-Dimensional Schrödinger Operators

2008 ◽  
Vol 283 (3) ◽  
pp. 853-860 ◽  
Author(s):  
Yuri Berest ◽  
Tim Cramer ◽  
Farkhod Eshmatov
Keyword(s):  
Heat Kernel ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Two Dimensional

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

Two-dimensional phase unwrapping using a minimum spanning tree algorithm

1992 ◽  
Vol 1 (3) ◽  
pp. 355-365 ◽  
Author(s):  
N.H. Ching ◽  
D. Rosenfeld ◽  
M. Braun
Keyword(s):  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Phase Unwrapping ◽  
Two Dimensional ◽  
Tree Algorithm
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