Random walks and harmonic functions on infinite planar graphs using square tilings

Annals of Probability

Volumn 24, Issue 3, 1996, Pages 1219-1238

  Benjamini, Itai ^a   Schramm, Oded ^b  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b NONE

Author keywords

Dirichlet problem; Harmonic measure; Planar graphs; Random walks

Indexed keywords

EID: 0030359763     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1065725179     Document Type: Article

References (6)

1. BENJAMINI, I. and SCHRAMM, O. (1995). Harmonic function on planar graphs and almost planar manifolds, via circle packings. Invent. Math. To appear.
2. BROOKS, R. L., SMITH, C. A. B., STONE, A. H. and TUTTE, W. T. (1940). The dissection of squares into squares. Duke Math. J. 7 312-340.
3. CANNON, J. W., FLOYD, W. J. and PARRY, W. R. (1994). Squaring rectangles: the finite Riemann mapping theorem. The Mathematical Heritage of Wilhelm Magnus - Groups, Geometry and Special Functions. Amer. Math. Soc., Providence, RI. To appear.
4. SCHRAMM, O. (1993). Square tilings with prescribed combinatorics. Israel J. Math. 84 97-118.
5. SOARDI, P. M. (1994). Potential Theory on Infinite Networks. Lecture Notes in Math. 1590 187. Springer, Berlin.
6. WOESS, W. (1994). Random walks on infinite graphs and groups - a survey on selected topics. Bull. London Math. Soc. 26 1-60.