@book{AST_2010__329__R1_0,
author = {L\'evy, Thierry},
title = {Two-dimensional {Markovian} holonomy fields},
series = {Ast\'erisque},
year = {2010},
publisher = {Soci\'et\'e math\'ematique de France},
number = {329},
mrnumber = {2667871},
zbl = {1200.60003},
language = {en},
url = {https://www.numdam.org/item/AST_2010__329__R1_0/}
}
Lévy, Thierry. Two-dimensional Markovian holonomy fields. Astérisque, no. 329 (2010), 178 p. https://www.numdam.org/item/AST_2010__329__R1_0/
[1] , & - Stochastic Lie group-valued measures and their relations to stochastic curve integrals, gauge fields and Markov cosurfaces, in Stochastic processes-mathematics and physics (Bielefeld, 1984), Lecture Notes in Math., vol. 1158, Springer, 1986, pp. 1-24. | MR | Zbl | DOI
[2] , & , Stochastic multiplicative measures, generalized Markov semigroups, and group-valued stochastic processes and fields, J. Funct. Anal., t. 78 (1988), pp. 154-184. | MR | Zbl | DOI
[3] & - Lévy flows on manifolds and Lévy processes on Lie groups, J. Math. Kyoto Univ., t. 33 (1993), pp. 1103-1123. | MR | Zbl | DOI
[4] - Topological quantum field theories., Publ. Math., Inst. Hautes Etud. Sci., t. 68 (1988), pp. 175-186. | MR | Zbl | EuDML | Numdam | DOI
[5] & - Gauge fields, knots and gravity, Series on Knots and Everything, vol. 4, World Scientific Publishing Co. Inc., 1994. | MR | Zbl
[6] & - A generalization of the isoperimetric inequality, J. Differential Geometry, t. 6 (1971/72), pp. 175-192. | MR | Zbl | DOI
[7] - Gauge theory and variational principles, Global Analysis Pure and Applied> Series A, vol. 1, Addison-Wesley Publishing Co., Reading, Mass., 1981. | MR | Zbl
[8] & - Two-dimensional gauge theories of the symmetric group in the large- limit, Comm. Math. Phys., t. 245 (2004), pp. 1-25. | MR | Zbl | DOI
[9] - Singular sets of minimizers for the Mumford-Shah functional, Progress in Math., vol. 233, Birkhäuser, 2005. | MR | Zbl
[10] - : continuum expectations, lattice convergence, and lassos, Comm. Math. Phys., t. 123 (1989), pp. 575-616. | MR | Zbl | DOI
[11] , Two-dimensional Euclidean quantized Yang-Mills fields, in Probability models in mathematical physics (Colorado Springs, CO, 1990), World Sci. Publ., Teaneck, NJ, 1991, pp. 21-36. | MR
[12] - The coding of compact real trees by real valued functions., Preprint (2006).
[13] - Quantum Yang-Mills on the two-sphere, Comm. Math. Phys., t. 134 (1990), pp. 273-292. | MR | Zbl | DOI
[14] , Quantum Yang-Mills on a Riemann surface, Comm. Math. Phys., t. 140 (1991), pp. 321-338. | MR | Zbl | DOI
[15] & - Loops, knots, gauge theories and quantum gravity, Cambridge Monographs on Mathematical Physics, Cambridge Univ. Press, 1996. | MR | Zbl
[16] & - Some properties of large- two-dimensional Yang-Mills theory, Nuclear Phys. B, t. 437 (1995), pp. 541-584. | MR | Zbl | DOI
[17] & - Two-dimensional is a string theory, Nuclear Phys. B, t. 400 (1993), pp. 181-208. | MR | Zbl | DOI
[18] - A Poincaré lemma for connection forms, J. Funct. Anal., t. 63 (1985), pp. 1-46. | MR | Zbl | DOI
[19] , The Maxwell equations for Yang-Mills theory, in Mathematical quantum field theory and related topics (Montreal, PQ, 1987), CMS Conf. Proc, vol. 9, Amer. Math. Soc, 1988, pp. 193-203. | MR | Zbl
[20] , & - Two-dimensional Yang-Mills theory via stochastic differential equations, Ann. Physics, t. 194 (1989), pp. 65-112. | MR | Zbl | DOI
[21] & - Uniqueness for the signature of a path of bounded variation and the reduced path group, Preprint (2006). | MR | Zbl
[22] & - Foundations of differential geometry. Vol. I, Wiley Classics Library, John Wiley & Sons Inc., 1996, Reprint of the 1963 original, A Wiley-Interscience Publication. | MR
[23] & - Graphs on surfaces and their applications, Encyclopaedia of Math. Sciences, vol. 141, Springer, 2004. | MR | Zbl | DOI
[24] - Yang-Mills measure on compact surfaces, Mem. Amer. Math. Soc., t. 166 (2003). | MR | Zbl
[25] , Discrete and continuous Yang-Mills measure for non-trivial bundles over compact surfaces, Probab. Theory Related Fields, t. 136 (2006), pp. 171-202. | MR | Zbl | DOI
[26] , Schur-Weyl duality and the heat kernel measure on the unitary group., Adv. Math., t. 218 (2008), pp. 537-575. | MR | Zbl | DOI
[27] - Lévy processes in Lie groups, Cambridge Tracts in Mathematics, vol. 162, Cambridge Univ. Press, 2004. | MR | Zbl
[28] & - Elements of Lipschitz topology, Ann. Acad. Sci. Fenn. Ser. A I Math., t. 3 (1977), pp. 85-122. | MR | Zbl | DOI
[29] & - Combinatorial group theory, Classics in Mathematics, Springer, 2001, Reprint of the 1977 edition. | MR | Zbl | DOI
[30] - Algebraic topology: an introduction, Springer, 1977, Reprint of the 1967 edition, Graduate Texts in Mathematics, Vol. 56. | MR | Zbl
[31] - Recursion equations in gauge field theories, Sov. Phys. JETP, t. 42 (1975), pp. 413-418.
[32] & - Graphs on surfaces, Johns Hopkins Studies in the Mathematical Sciences, Johns Hopkins University Press, 2001. | MR | Zbl
[33] - Geometric topology in dimensions and , Springer, 1977, Graduate Texts in Mathematics, Vol. 47. | MR | Zbl
[34] - The Yang-Mills measure for , J. Funct. Anal., t. 108 (1992), pp. 231-273. | MR | Zbl | DOI
[35] , Gauge theory on compact surfaces, Mem. Amer. Math. Soc, t. 126 (1997). | MR | Zbl
[36] - The topology of fibre bundles, Princeton Landmarks in Mathematics, Princeton Univ. Press, 1999, Reprint of the 1957 edition, Princeton Paperbacks. | MR | Zbl
[37] - The isoperimetric inequality for curves with self-intersections, Canad. Math. Bull., t. 24 (1981), pp. 161-167. | MR | Zbl | DOI
[38] - Topology of Manifolds, American Mathematical Society Colloquium Publications, vol. 32, Amer. Math. Soc., 1949. | MR | Zbl | DOI
[39] - On quantum gauge theories in two dimensions, Comm. Math. Phys., t. 141 (1991), pp. 153-209. | MR | Zbl | DOI
[40] , Two-dimensional gauge theories revisited, J. Geom. Phys., t. 9 (1992), pp. 303-368. | MR | Zbl | DOI
[41] & - Conservation of isotopic spin and isotopic gauge invariance, Physical Rev., t. 96 (1954), pp. 191-195. | MR | Zbl | DOI
[42] - An inequality of the Hölder type, connected with Stieltjes integration, Acta Math., t. 67 (1936), pp. 251-282. | MR | Zbl | JFM | DOI






