Circle-packing connections with random walks and a finite volume method
Séminaire de théorie spectrale et géométrie, Tome 15 (1996-1997), pp. 153-161.
@article{TSG_1996-1997__15__153_0,
     author = {Dubejko, Tomasz},
     title = {Circle-packing connections with random walks and a finite volume method},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {153--161},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {15},
     year = {1996-1997},
     zbl = {0912.52010},
     language = {en},
     url = {http://www.numdam.org/item/TSG_1996-1997__15__153_0/}
}
TY  - JOUR
AU  - Dubejko, Tomasz
TI  - Circle-packing connections with random walks and a finite volume method
JO  - Séminaire de théorie spectrale et géométrie
PY  - 1996-1997
DA  - 1996-1997///
SP  - 153
EP  - 161
VL  - 15
PB  - Institut Fourier
PP  - Grenoble
UR  - http://www.numdam.org/item/TSG_1996-1997__15__153_0/
UR  - https://zbmath.org/?q=an%3A0912.52010
LA  - en
ID  - TSG_1996-1997__15__153_0
ER  - 
Dubejko, Tomasz. Circle-packing connections with random walks and a finite volume method. Séminaire de théorie spectrale et géométrie, Tome 15 (1996-1997), pp. 153-161. http://www.numdam.org/item/TSG_1996-1997__15__153_0/

[BeSc] I. Benjamini and O. Schramm. - Harmonic fonctions on planar and almost planar graphs and manifolds, via circlepackings. Invent. Math. 126 ( 1996), 565-587. | Zbl 0868.31008

[BoSt] P. L. Bowers and K. Stephenson. - A branched Andreev-Thurston theorem for circle packings on the sphere, Proc. London Math. Soc. 73( 1996), 185-215. | Zbl 0856.51012

[BR] R. E. Bank and D. J. Rosé. - Some error estimates for the box method, SIAM J. Numer. Anal. 24 ( 1987), 777-787. | Zbl 0634.65105

[BSt1] A. F. Beardon and K. Stephenson. - The uniformization theorem for circle packings, Indiana Univ. Math. J. 39 ( 1990), 1383-1425. | MR 1087197 | Zbl 0797.30008

[BSt2] A. F. Beardon and K. Stephenson.- The Schwarz-Pick lemma for circle packings, 111. J. Math. 141 ( 1991), 577-606. | MR 1115988 | Zbl 0753.30016

[C] Z. Cal - On the unite volume element method, Numer. Math. 58 ( 1991), 713-735. | MR 1090257 | Zbl 0731.65093

[CdV] Y. Colin De Verdière. - Un principe variationnel pour les empilements de cercles, Invent. Math. 104 ( 1991), 655-669. | MR 1106755 | Zbl 0745.52010

[CdVMa] Y. Colin De Verdière and F. Mathéus. - Empilements de cercles et approximations conformes, Actes de la Table Ronde de Géométrie Riemannienne en l'honneur de Marcel Berger, A. L. Besse (éditeur), Collection SMF Séminaires et Congrès 1 ( 1996), 253-272. | MR 1427761 | Zbl 0932.52004

[CMM] Z. Cai, J. Mandel and S. Mccormick. - The finite volume element method for diffusion equations on general triangulations, SIAM J. Numer. Anal. 28 ( 1991), 392-402. | MR 1087511 | Zbl 0729.65086

[De] D. R. Debaun.- L2-cohomology of noncompact surfaces, Proc. Amer. Math. Soc. 284 ( 1984), 543-565. | MR 743732 | Zbl 0511.58002

[DoSn] P. Doyle and J. Snell. - Random walks and electric networks, Carus Mathematica! Monographs, 22, MAA, 1984. | MR 920811 | Zbl 0583.60065

[D1] T. Dubejko. - Branched circle packings and discrete Blaschke products, Trans. Amer. Math. Soc. 347 ( 1995). 4073-1103. | MR 1308008 | Zbl 0849.30028

[D2] T. Dubejko. - Recurrent random walks, Liouville's theorem, and circle packing, Math. Proc. Cambridge Philos. Soc. 121 ( 1997), 531-546. | MR 1434659 | Zbl 0888.30005

[D3] T. Dubejko. - Random walks on circle packings, (Math Sci Res Inst preprint #066-95), Contemp. Math., (to appear). | MR 1476986 | Zbl 0898.60072

[D4] T. Dubejko. - Discrete solutions of Dirichlet problems, finite volumes, and circle packings, preprint. | MR 1692623 | Zbl 0945.30004

[ECH] R. Eymard, T. Gallouët and R. Herbin. - Finite Volume Methods, in preparation for the Handbook of Numerical Analysis, Ph. Ciarlet and J. L. Lions eds. | Zbl 0981.65095

[Ha] W. Hackbusch. - On first and second order box schemes, Computing 41 ( 1989), 277-296. | MR 993825 | Zbl 0649.65052

[Hn] B. Heinrich. - Finite difference methods on irregular networks, Birkhäuser-Verlag, 1987. | MR 875416 | Zbl 0623.65096

[HSc1] Z.-X. He and O. Schramm. - Fixed points, Koebe uniformization and circle packings, Ann. of Math. 137 ( 1993). 369-406. | MR 1207210 | Zbl 0777.30002

[HSc2] Z.-X. He and O. Schramm. - Hyperbolic and parabolic packings, Discrete and Comput. Geom. 14 (95). 123-149. | MR 1331923 | Zbl 0830.52010

[HSc3] Z.-X. He and O. Schramm. - On convergence of circle packings to the Riemann map, Invent. Math. 125 ( 1996), 285-305. | MR 1395721 | Zbl 0868.30010

[HR] Z.-X. He and B. Rodin. - Convergence of circle packings of finite valence to Riemann mappings, Comm. in Analysis and Geometry 1 ( 1993), 31-41. | MR 1230272 | Zbl 0777.30003

[Ma] F. Mathéus. - Empilements de cercles et discrétisation quasiconforme: comportement asymptotique des rayons. preprint. | MR 1692619 | Zbl 0930.30011

[Mc] G. Mccaughan. - A recurrence/transience resuit for circle packings, Proc. Amer. Math. Soc, (to appear). | MR 1327026 | Zbl 0912.30002

[RS] B. Rodin and D. Sullivan. - The convergence of circle packings to the Riemann mapping, J. Differential Geom. 26 ( 1987). 349-360. | MR 906396 | Zbl 0694.30006

[S] P. M. Soardi. - Potential theory on infinite networks, Lecture notes in mathematics, 1590, Springer-Verlag, 1994. | MR 1324344 | Zbl 0818.31001

[St1] K. Stephenson. - Circle packings in the approximation of conformal mappings, Bull. Amer. Math. Soc. (Research Announcements) 23, (2) ( 1990), 407-115. | MR 1049434 | Zbl 0714.30011

[St2] K. Stephenson. - A probabilistic proof of Thurston's conjecture on circle packings, Rend. Sem. Mat. Fis. Milano, (to appear). | MR 1639851 | Zbl 0997.60504

[St3] K. Stephenson. - CirclePack (software), http://www.math.utk.edu/~kens.

[Th1] W.P. Thurston. - The Geometry and Topology of 3-ManifoIds, Princeton University Notes, Princeton University Press, 1980.

[Th2] W.P. Thurston. - The finite Riemann mapping theorem, Invited talk, An International Symposium at Purdue University on the occasion of the proof of the Bieberbach conjecture, March 1985.

[W] W. Woess. - Random walks on infinite graphs and groups - a survey on selected topics, Bull. London Math. Soc. 26 ( 1994), 1-60. | MR 1246471 | Zbl 0830.60061