Đặc trưng hóa sự thu gọn hình méo của không gian $$L_{p}$$ bằng các phép đo ngẫu nhiên
Tóm tắt
Chúng tôi trình bày một đặc trưng hoàn chỉnh về sự thu gọn hình méo của không gian
Từ khóa
Tài liệu tham khảo
Abate, M., Raissy, J.: Wolff-Denjoy theorems in nonsmooth convex domains. Ann. Mat. Pura Appl. 193(5), 1503–1518 (2014). (4)
Albiac, F., Kalton, N.J.: Topics in Banach Space Theory 2nd Ed., volume 233 of Graduate Texts in Mathematics. Springer, Cham (2016)
Aldous, D.J.: Subspaces of $$L^{1}$$, via random measures. Trans. Am. Math. Soc. 267(2), 445–463 (1981)
Alessandrini, D., Liu, L., Papadopoulos, A., Su, W.: The horofunction compactification of Teichmüller spaces of surfaces with boundary. Topol. Appl. 208, 160–191 (2016)
Auffinger, A., Damron, M., Hanson, J.: Limiting geodesics for first-passage percolation on subsets of $${\mathbb{Z}}^2$$. Ann. Appl. Probab. 25(1), 373–405 (2015)
Ballmann, W., Gromov, M., Schroeder, V.: Manifolds of Nonpositive Curvature, Volume 61 of Progress in Mathematics. Birkhäuser Boston, Inc., Boston (1985)
Björklund, M.: Central limit theorems for Gromov hyperbolic groups. J. Theor. Probab. 23(3), 871–887 (2010)
Budzyńska, M., Kuczumow, T., Reich, S.: Theorems of Denjoy-Wolff type. Ann. Math. Pura Appl. 192(4), 621–648 (2013). (4)
Crauel, H.: Random Probability Measures on Polish spaces, Volume 11 of Stochastics Monographs. Taylor & Francis, London (2002)
D’Angeli, D., Donno, A.: Metric compactification of infinite Sierpiński carpet graphs. Discrete Math. 339(11), 2693–2705 (2016)
Dunford, N., Schwartz, J.T.: Linear operators. I. General theory. In: Bade, W.G., Bartle, R.G. (eds.) Pure and Applied Mathematics, vol. 7. Interscience Publishers, New York (1958). (Interscience Publishers, Ltd., London )
Edwards, R.E.: Functional analysis: theory and applications. Corrected reprint of the 1965 original. Dover Publications, Inc., New York (1995)
Garling, D.J.H.: Stable Banach spaces, random measures and Orlicz function spaces. In: Heyer H. (ed) Probability Measures on Groups. Lecture Notes in Mathematics, pp. 121–175. Springer, Berlin, Heidelberg (1982)
Gaubert, S., Vigeral, G.: A maximin characterisation of the escape rate of non-expansive mappings in metrically convex spaces. Math. Proc. Camb. Philos. Soc. 152(2), 341–363 (2012)
Gouëzel, S.: Subadditive cocycles and horofunctions. In: Proceedings of the International Congress of Mathematicians (ICM 2018)
Gouëzel, S.: Analyticity of the entropy and the escape rate of random walks in hyperbolic groups. Discrete Anal., pages Paper No. 7, 37, (2017)
Gouëzel, S., Karlsson, A.: Subadditive and multiplicative ergodic theorems. arXiv:1509.07733 (2015)
Gromov, M.: Hyperbolic manifolds, groups and actions. In: Kra, I., Maskit, B. (eds.) Riemann Surfaces and Related Topics, vol. 97, pp. 183–213. Ann. of Math. Stud. Princeton Univ. Press, Princeton (1981)
Gutiérrez, A.W.: On the metric compactification of infinite–dimensional $$\ell _p$$ spaces. Canad. Math. Bull. 62(3), 491–507 (2019)
Gutiérrez, A.W.: The horofunction boundary of finite-dimensional $$\ell _p$$ spaces. Colloq. Math. 155(1), 51–65 (2019)
Kallenberg, O.: Random Measures, Theory and Applications, volume 77 of Probability Theory and Stochastic Modelling. Springer, Cham (2017)
Karlsson, A., Metz, V., Noskov, G.A.: Horoballs in simplices and Minkowski spaces. Int. J. Math. Math. Sci. 20, 23656 (2006)
Karlsson, A.: Non-expanding maps and Busemann functions. Ergodic Theory Dyn. Syst. 21(5), 1447–1457 (2001)
Karlsson, A.: Dynamics of Hilbert nonexpansive maps. In: Papadopoulos, A., Troyanov, M. (eds.) Handbook of Hilbert geometry, pp. 263–273. Eur. Math. Soc., Zürich (2014)
Karlsson, A.: Elements of a metric spectral theory. arXiv:1904.01398, (2018)
Karlsson, A., Ledrappier, F.: Noncommutative ergodic theorems. In: Farb, B., Fisher, D. (eds.) Geometry, Rigidity, and Group Actions, Chicago Lectures in Math., pp. 396–418. Univ. Chicago Press, Chicago (2011)
Karlsson, A., Margulis, G.A.: A multiplicative ergodic theorem and nonpositively curved spaces. Commun. Math. Phys. 208(1), 107–123 (1999)
Klein, T., Nicas, A.: The horofunction boundary of the Heisenberg group. Pac. J. Math. 242(2), 299–310 (2009)
Lemmens, B., Lins, B., Nussbaum, R., Wortel, M.: Denjoy-Wolff theorems for Hilbert’s and Thompson’s metric spaces. J. Anal. Math. 134(2), 671–718 (2018)
Lemmens, B., Walsh, C.: Isometries of polyhedral Hilbert geometries. J. Topol. Anal. 3(2), 213–241 (2011)
Ji, L., Schilling, A.: Toric varieties vs. horofunction compactifications of polyhedral norms. Enseign. Math. 63(3–4), 375–401 (2017)
Maher, J., Tiozzo, G.: Random walks on weakly hyperbolic groups. Journal für die reine und angewandte Mathematik (Crelles Journal) 2018(742), 187–239 (2016)
Rieffel, M.A.: Group $$C^*$$-algebras as compact quantum metric spaces. Doc. Math. 7, 605–651 (2002)
Walsh, C.: The horofunction boundary of finite-dimensional normed spaces. Math. Proc. Camb. Philos. Soc. 142(3), 497–507 (2007)
Walsh, C.: The action of a nilpotent group on its horofunction boundary has finite orbits. Groups Geom. Dyn. 5(1), 189–206 (2011)
Walsh, C.: The horoboundary and isometry group of Thurston’s Lipschitz metric. In: Papadopoulos, A. (ed.) Handbook of Teichmüller Theory, vol. IV, pp. 327–353. Eur. Math. Soc., Zürich (2014)
Walsh, C.: The horofunction boundary and isometry group of the Hilbert geometry. In: Papadopoulos, A., Troyanov, M. (eds.) Handbook of Hilbert Geometry, pp. 127–146. Eur. Math. Soc., Zürich (2014)