Two-dimensional Markovian holonomy fields
Astérisque, no. 329 (2010) , 178 p.
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@book{AST_2010__329__R1_0,
author = {L\'evy, Thierry},
title = {Two-dimensional Markovian holonomy fields},
series = {Ast\'erisque},
publisher = {Soci\'et\'e math\'ematique de France},
number = {329},
year = {2010},
zbl = {1200.60003},
mrnumber = {2667871},
language = {en},
url = {http://www.numdam.org/item/AST_2010__329__R1_0}
}

Lévy, Thierry. Two-dimensional Markovian holonomy fields. Astérisque, no. 329 (2010), 178 p. http://www.numdam.org/item/AST_2010__329__R1_0/

[1] Albeverio (Sergio), Høegh-Krohn (Raphael) & Holden (Helge) - 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. | Article | MR 838556 | Zbl 0575.60068

[2] Albeverio (Sergio), Høegh-Krohn (Raphael) & Holden (Helge), Stochastic multiplicative measures, generalized Markov semigroups, and group-valued stochastic processes and fields, J. Funct. Anal., t. 78 (1988), pp. 154-184. | Article | MR 937637 | Zbl 0639.60010

[3] Applebaum (David) & Kunita (Hiroshi) - Lévy flows on manifolds and Lévy processes on Lie groups, J. Math. Kyoto Univ., t. 33 (1993), pp. 1103-1123. | Article | MR 1251218 | Zbl 0804.58057

[4] Atiyah (Michael) - Topological quantum field theories., Publ. Math., Inst. Hautes Etud. Sci., t. 68 (1988), pp. 175-186. | Article | Numdam | MR 1001453 | Zbl 0692.53053

[5] Baez (John) & Muniain (Javier P.) - Gauge fields, knots and gravity, Series on Knots and Everything, vol. 4, World Scientific Publishing Co. Inc., 1994. | MR 1313910 | Zbl 0843.57001

[6] Banchoff (Thomas F.) & Pohl (William F.) - A generalization of the isoperimetric inequality, J. Differential Geometry, t. 6 (1971/72), pp. 175-192. | Article | MR 305319 | Zbl 0227.53040

[7] Bleecker (David) - Gauge theory and variational principles, Global Analysis Pure and Applied> Series A, vol. 1, Addison-Wesley Publishing Co., Reading, Mass., 1981. | MR 643361 | Zbl 0481.58002

[8] D'Adda (Alessandro) & Provero (Paolo) - Two-dimensional gauge theories of the symmetric group ${S}_{n}$ in the large-$n$ limit, Comm. Math. Phys., t. 245 (2004), pp. 1-25. | Article | MR 2036366 | Zbl 1069.81033

[9] David (Guy) - Singular sets of minimizers for the Mumford-Shah functional, Progress in Math., vol. 233, Birkhäuser, 2005. | MR 2129693 | Zbl 1086.49030

[10] Driver (Bruce K.) - $Y{M}_{2}$: continuum expectations, lattice convergence, and lassos, Comm. Math. Phys., t. 123 (1989), pp. 575-616. | Article | MR 1006295 | Zbl 0819.58043

[11] Driver (Bruce K.), 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 1120553

[12] Duquesne (Thomas) - The coding of compact real trees by real valued functions., Preprint (2006).

[13] Fine (Dana S.) - Quantum Yang-Mills on the two-sphere, Comm. Math. Phys., t. 134 (1990), pp. 273-292. | Article | MR 1081007 | Zbl 0715.58046

[14] Fine (Dana S.), Quantum Yang-Mills on a Riemann surface, Comm. Math. Phys., t. 140 (1991), pp. 321-338. | Article | MR 1124272 | Zbl 0734.53069

[15] Gambini (Rodolfo) & Pullin (Jorge) - Loops, knots, gauge theories and quantum gravity, Cambridge Monographs on Mathematical Physics, Cambridge Univ. Press, 1996. | MR 1439964 | Zbl 0865.53064

[16] Gross (David J.) & Matytsin (Andrei) - Some properties of large-$N$ two-dimensional Yang-Mills theory, Nuclear Phys. B, t. 437 (1995), pp. 541-584. | Article | MR 1321333 | Zbl 1052.81560

[17] Gross (David J.) & Taylor (Washington Iv) - Two-dimensional $QCD$ is a string theory, Nuclear Phys. B, t. 400 (1993), pp. 181-208. | Article | MR 1227260 | Zbl 0941.81586

[18] Gross (Leonard) - A Poincaré lemma for connection forms, J. Funct. Anal., t. 63 (1985), pp. 1-46. | Article | MR 795515 | Zbl 0624.53021

[19] Gross (Leonard), 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 973470 | Zbl 0651.53023

[20] Gross (Leonard), King (Christopher) & Sengupta (Ambar N.) - Two-dimensional Yang-Mills theory via stochastic differential equations, Ann. Physics, t. 194 (1989), pp. 65-112. | Article | MR 1015789 | Zbl 0698.60047

[21] Hambly (Ben) & Lyons (Terry J.) - Uniqueness for the signature of a path of bounded variation and the reduced path group, Preprint (2006). | MR 2630037 | Zbl 1276.58012

[22] Kobayashi (Shoshichi) & Nomizu (Katsumi) - Foundations of differential geometry. Vol. I, Wiley Classics Library, John Wiley & Sons Inc., 1996, Reprint of the 1963 original, A Wiley-Interscience Publication. | MR 1393940

[23] Lando (Sergei K.) & Zvonkin (Alexander K.) - Graphs on surfaces and their applications, Encyclopaedia of Math. Sciences, vol. 141, Springer, 2004. | Article | MR 2036721 | Zbl 1040.05001

[24] Lévy (Thierry) - Yang-Mills measure on compact surfaces, Mem. Amer. Math. Soc., t. 166 (2003). | MR 2006374 | Zbl 1036.58009

[25] Lévy (Thierry), Discrete and continuous Yang-Mills measure for non-trivial bundles over compact surfaces, Probab. Theory Related Fields, t. 136 (2006), pp. 171-202. | Article | MR 2240786 | Zbl 1103.81033

[26] Lévy (Thierry), Schur-Weyl duality and the heat kernel measure on the unitary group., Adv. Math., t. 218 (2008), pp. 537-575. | Article | MR 2407946 | Zbl 1147.60053

[27] Liao (Ming) - Lévy processes in Lie groups, Cambridge Tracts in Mathematics, vol. 162, Cambridge Univ. Press, 2004. | MR 2060091 | Zbl 1076.60004

[28] Luukkainen (Jouni) & Väisälä (Jussi) - Elements of Lipschitz topology, Ann. Acad. Sci. Fenn. Ser. A I Math., t. 3 (1977), pp. 85-122. | Article | MR 515647 | Zbl 0397.57011

[29] Lyndon (Roger C.) & Schupp (Paul E.) - Combinatorial group theory, Classics in Mathematics, Springer, 2001, Reprint of the 1977 edition. | Article | MR 1812024 | Zbl 0997.20037

[30] Massey (William S.) - Algebraic topology: an introduction, Springer, 1977, Reprint of the 1967 edition, Graduate Texts in Mathematics, Vol. 56. | MR 448331 | Zbl 0457.55001

[31] Migdal (Alexander A. ) - Recursion equations in gauge field theories, Sov. Phys. JETP, t. 42 (1975), pp. 413-418.

[32] Mohar (Bojan) & Thomassen (Carsten) - Graphs on surfaces, Johns Hopkins Studies in the Mathematical Sciences, Johns Hopkins University Press, 2001. | MR 1844449 | Zbl 0979.05002

[33] Moise (Edwin E.) - Geometric topology in dimensions $2$ and $3$, Springer, 1977, Graduate Texts in Mathematics, Vol. 47. | MR 488059 | Zbl 0349.57001

[34] Sengupta (Ambar N.) - The Yang-Mills measure for ${S}^{2}$, J. Funct. Anal., t. 108 (1992), pp. 231-273. | Article | MR 1176676 | Zbl 0769.60009

[35] Sengupta (Ambar N.), Gauge theory on compact surfaces, Mem. Amer. Math. Soc, t. 126 (1997). | MR 1346931 | Zbl 0873.58076

[36] Steenrod (Norman) - The topology of fibre bundles, Princeton Landmarks in Mathematics, Princeton Univ. Press, 1999, Reprint of the 1957 edition, Princeton Paperbacks. | MR 1688579 | Zbl 0942.55002

[37] Vogt (Andrew) - The isoperimetric inequality for curves with self-intersections, Canad. Math. Bull., t. 24 (1981), pp. 161-167. | Article | MR 619441 | Zbl 0466.52009

[38] Wilder (Raymond L.) - Topology of Manifolds, American Mathematical Society Colloquium Publications, vol. 32, Amer. Math. Soc., 1949. | Article | MR 29491 | Zbl 0039.39602

[39] Witten (Edward) - On quantum gauge theories in two dimensions, Comm. Math. Phys., t. 141 (1991), pp. 153-209. | Article | MR 1133264 | Zbl 0762.53063

[40] Witten (Edward), Two-dimensional gauge theories revisited, J. Geom. Phys., t. 9 (1992), pp. 303-368. | Article | MR 1185834 | Zbl 0768.53042

[41] Yang (Chen N. ) & Mills (Robert L.) - Conservation of isotopic spin and isotopic gauge invariance, Physical Rev., t. 96 (1954), pp. 191-195. | Article | MR 65437 | Zbl 1378.81075

[42] Young (Laurence C.) - An inequality of the Hölder type, connected with Stieltjes integration, Acta Math., t. 67 (1936), pp. 251-282. | Article | JFM 62.0250.02 | MR 1555421 | Zbl 0016.10404