Two-dimensional Markovian holonomy fields

Lévy, Thierry

Astérisque, no. 329 (2010) , 178 p.

MR Zbl

@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},
     mrnumber = {2667871},
     zbl = {1200.60003},
     language = {en},
     url = {http://archive.numdam.org/item/AST_2010__329__R1_0/}
}

TY  - BOOK
AU  - Lévy, Thierry
TI  - Two-dimensional Markovian holonomy fields
T3  - Astérisque
PY  - 2010
IS  - 329
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_2010__329__R1_0/
LA  - en
ID  - AST_2010__329__R1_0
ER  -

%0 Book
%A Lévy, Thierry
%T Two-dimensional Markovian holonomy fields
%S Astérisque
%D 2010
%N 329
%I Société mathématique de France
%U http://archive.numdam.org/item/AST_2010__329__R1_0/
%G en
%F AST_2010__329__R1_0

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

Bibliographie
Cité par

[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. | MR | Zbl | DOI

[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. | MR | Zbl | DOI

[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. | MR | Zbl | DOI

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

[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 | Zbl

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

[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 | Zbl

[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. | MR | Zbl | DOI

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

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

[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

[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. | MR | Zbl | DOI

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

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

[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. | MR | Zbl | DOI

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

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

[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 | Zbl

[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. | MR | Zbl | DOI

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

[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

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

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

[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. | MR | Zbl | DOI

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

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

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

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

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

[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 | Zbl

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

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

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

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

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

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

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

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

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

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