@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 SP - 153 EP - 161 VL - 15 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/item/TSG_1996-1997__15__153_0/ LA - en ID - TSG_1996-1997__15__153_0 ER -
%0 Journal Article %A Dubejko, Tomasz %T Circle-packing connections with random walks and a finite volume method %J Séminaire de théorie spectrale et géométrie %D 1996-1997 %P 153-161 %V 15 %I Institut Fourier %C Grenoble %U http://www.numdam.org/item/TSG_1996-1997__15__153_0/ %G en %F TSG_1996-1997__15__153_0
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] Harmonic fonctions on planar and almost planar graphs and manifolds, via circlepackings. Invent. Math. 126 ( 1996), 565-587. | Zbl
and . -[BoSt] A branched Andreev-Thurston theorem for circle packings on the sphere, Proc. London Math. Soc. 73( 1996), 185-215. | Zbl
and . -[BR] Some error estimates for the box method, SIAM J. Numer. Anal. 24 ( 1987), 777-787. | Zbl
and . -[BSt1] The uniformization theorem for circle packings, Indiana Univ. Math. J. 39 ( 1990), 1383-1425. | MR | Zbl
and . -[BSt2] The Schwarz-Pick lemma for circle packings, 111. J. Math. 141 ( 1991), 577-606. | MR | Zbl
and .-[C] On the unite volume element method, Numer. Math. 58 ( 1991), 713-735. | MR | Zbl
-[CdV] Un principe variationnel pour les empilements de cercles, Invent. Math. 104 ( 1991), 655-669. | MR | Zbl
. -[CdVMa] 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 | Zbl
and . -[CMM] The finite volume element method for diffusion equations on general triangulations, SIAM J. Numer. Anal. 28 ( 1991), 392-402. | MR | Zbl
, and . -[De] L2-cohomology of noncompact surfaces, Proc. Amer. Math. Soc. 284 ( 1984), 543-565. | MR | Zbl
.-[DoSn] Random walks and electric networks, Carus Mathematica! Monographs, 22, MAA, 1984. | MR | Zbl
and . -[D1] Branched circle packings and discrete Blaschke products, Trans. Amer. Math. Soc. 347 ( 1995). 4073-1103. | MR | Zbl
. -[D2] Recurrent random walks, Liouville's theorem, and circle packing, Math. Proc. Cambridge Philos. Soc. 121 ( 1997), 531-546. | MR | Zbl
. -[D3] Random walks on circle packings, (Math Sci Res Inst preprint #066-95), Contemp. Math., (to appear). | MR | Zbl
. -[D4] Discrete solutions of Dirichlet problems, finite volumes, and circle packings, preprint. | MR | Zbl
. -[ECH] Finite Volume Methods, in preparation for the Handbook of Numerical Analysis, Ph. Ciarlet and J. L. Lions eds. | Zbl
, and . -[Ha] On first and second order box schemes, Computing 41 ( 1989), 277-296. | MR | Zbl
. -[Hn] Finite difference methods on irregular networks, Birkhäuser-Verlag, 1987. | MR | Zbl
. -[HSc1] Fixed points, Koebe uniformization and circle packings, Ann. of Math. 137 ( 1993). 369-406. | MR | Zbl
and . -[HSc2] Hyperbolic and parabolic packings, Discrete and Comput. Geom. 14 (95). 123-149. | MR | Zbl
and . -[HSc3] On convergence of circle packings to the Riemann map, Invent. Math. 125 ( 1996), 285-305. | MR | Zbl
and . -[HR] Convergence of circle packings of finite valence to Riemann mappings, Comm. in Analysis and Geometry 1 ( 1993), 31-41. | MR | Zbl
and . -[Ma] Empilements de cercles et discrétisation quasiconforme: comportement asymptotique des rayons. preprint. | MR | Zbl
. -[Mc] A recurrence/transience resuit for circle packings, Proc. Amer. Math. Soc, (to appear). | MR | Zbl
. -[RS] The convergence of circle packings to the Riemann mapping, J. Differential Geom. 26 ( 1987). 349-360. | MR | Zbl
and . -[S] Potential theory on infinite networks, Lecture notes in mathematics, 1590, Springer-Verlag, 1994. | MR | Zbl
. -[St1] Circle packings in the approximation of conformal mappings, Bull. Amer. Math. Soc. (Research Announcements) 23, (2) ( 1990), 407-115. | MR | Zbl
. -[St2] A probabilistic proof of Thurston's conjecture on circle packings, Rend. Sem. Mat. Fis. Milano, (to appear). | MR | Zbl
. -[St3] CirclePack (software), http://www.math.utk.edu/~kens.
. -[Th1] The Geometry and Topology of 3-ManifoIds, Princeton University Notes, Princeton University Press, 1980.
. -[Th2] 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] Random walks on infinite graphs and groups - a survey on selected topics, Bull. London Math. Soc. 26 ( 1994), 1-60. | MR | Zbl
. -