Download this PDF file Fullscreen Fullscreen Off
References
- Aigner, Martin; Ziegler, Günter M. Proofs from The Book.Including illustrations by Karl H. Hofmann.Third edition.Springer-Verlag, Berlin, 2004. viii+239 pp. ISBN: 3-540-40460-0 MR2014872 (2004h:00002)
- Bertin, Etienne; Billiot, Jean-Michel; Drouilhet, Rémy. Existence of ``nearest-neighbour'' spatial Gibbs models. Adv. in Appl. Probab. 31 (1999), no. 4, 895--909. MR1747447 (2001c:60015)
- Bertin, Etienne; Billiot, Jean-Michel; Drouilhet, Rémy. Existence of Delaunay pairwise Gibbs point process with superstable component. J. Statist. Phys. 95 (1999), no. 3-4, 719--744. MR1700922 (2000f:60069)
- Bertin, Etienne; Billiot, Jean-Michel; Drouilhet, Rémy. Phase transition in the nearest-neighbor continuum Potts model. J. Statist. Phys. 114 (2004), no. 1-2, 79--100. MR2032125 (2005h:82037)
- Bertin, Etienne; Billiot, Jean-Michel; Drouilhet, Rémy. $R$-local Delaunay inhibition model. J. Stat. Phys. 132 (2008), no. 4, 649--667. MR2429701
- Dembo, Amir; Zeitouni, Ofer. Large deviations techniques and applications.Second edition.Applications of Mathematics (New York), 38. Springer-Verlag, New York, 1998. xvi+396 pp. ISBN: 0-387-98406-2 MR1619036 (99d:60030)
- Dereudre, David. Gibbs Delaunay tessellations with geometric hardcore conditions. J. Stat. Phys. 131 (2008), no. 1, 127--151. MR2394701 (2009g:60016)
- Dereudre. D, Drouilhet. R and H.-O. Georgii, Existence of Gibbsian graphs for stable interactions, in preparation.
- Fritz, J. Generalization of McMillan's theorem to random set functions. Studia Sci. Math. Hungar. 5 (1970), 369--394. MR0293956 (45 #3031)
- Georgii, Hans-Otto. Gibbs measures and phase transitions.de Gruyter Studies in Mathematics, 9. Walter de Gruyter & Co., Berlin, 1988. xiv+525 pp. ISBN: 0-89925-462-4 MR0956646 (89k:82010)
- Georgii, Hans-Otto. Large deviations and maximum entropy principle for interacting random fields on $Zsp d$. Ann. Probab. 21 (1993), no. 4, 1845--1875. MR1245292 (94m:60061)
- Georgii H.O. Large deviations and the equivalence of ensembles for Gibbsian particle systems with superstable interaction, Probab. Theory Relat. Fields 99:171--195 (1994).
- Georgii, Hans-Otto. The equivalence of ensembles for classical systems of particles. J. Statist. Phys. 80 (1995), no. 5-6, 1341--1378. MR1349785 (96m:82003)
- Georgii, Hans-Otto; Zessin, Hans. Large deviations and the maximum entropy principle for marked point random fields. Probab. Theory Related Fields 96 (1993), no. 2, 177--204. MR1227031 (94j:60053)
- Grimmett, Geoffrey. Potts models and random-cluster processes with many-body interactions. J. Statist. Phys. 75 (1994), no. 1-2, 67--121. MR1273054 (96a:60079)
- Holley, R. A.; Stroock, D. W. Nearest neighbor birth and death processes on the real line. Acta Math. 140 (1978), no. 1-2, 103--154. MR0488380 (58 #7928)
- J. M¯ller, Lectures on Random Voronoi Tessellations, Lecture Notes in Statistics Vol. 87, Springer, Berlin etc., 1994.
- Nguyen, Xuan-Xanh; Zessin, Hans. Ergodic theorems for spatial processes. Z. Wahrsch. Verw. Gebiete 48 (1979), no. 2, 133--158. MR0534841 (81e:60061)
- Preston, Chris. Random fields.Lecture Notes in Mathematics, Vol. 534. Springer-Verlag, Berlin-New York, 1976. ii+200 pp. MR0448630 (56 #6936)
- Schneider, Rolf; Weil, Wolfgang. Stochastic and integral geometry.Probability and its Applications (New York). Springer-Verlag, Berlin, 2008. xii+693 pp. ISBN: 978-3-540-78858-4 MR2455326
- Zessin, H. Specific index and curvature of random simplicial complexes. Izv. Nats. Akad. Nauk Armenii Mat. 37 (2002), no. 1, 70--88 (2003); translation in J. Contemp. Math. Anal. 37 (2002), no. 1, 64--81 MR1964589 (2004b:60093)

This work is licensed under a Creative Commons Attribution 3.0 License.