Uniqueness of Gibbs measures relative to brownian motion
Betz, Volker ; Lőrinczi, József
Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003), p. 877-889 / Harvested from Numdam
@article{AIHPB_2003__39_5_877_0,
     author = {Betz, Volker and L\H orinczi, J\'ozsef},
     title = {Uniqueness of Gibbs measures relative to brownian motion},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {39},
     year = {2003},
     pages = {877-889},
     doi = {10.1016/S0246-0203(03)00021-9},
     mrnumber = {1997216},
     zbl = {1025.60043},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2003__39_5_877_0}
}
Betz, Volker; Lőrinczi, József. Uniqueness of Gibbs measures relative to brownian motion. Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) pp. 877-889. doi : 10.1016/S0246-0203(03)00021-9. http://gdmltest.u-ga.fr/item/AIHPB_2003__39_5_877_0/

[1] G. Benfatto, E. Presutti, M. Pulvirenti, DLR Measures for one-dimensional harmonic systems, Z. Wahr. Geb. 41 (1978) 305-312. | MR 467969 | Zbl 0355.60063

[2] V. Betz, Existence of Gibbs measures relative to Brownian motion, Markov Proc. Related Fields 1 (2002) 1-1, To appear. | MR 1973322 | Zbl 1017.60041

[3] V. Betz, F. Hiroshima, J. Lőrinczi, R.A. Minlos, H. Spohn, Ground state properties of the Nelson Hamiltonian - A Gibbs measure-based approach, Rev. Math. Phys. 14 (2002) 173-198. | Zbl 1029.81022

[4] K. Broderix, D. Hundertmark, H. Leschke, Continuity properties of Schrödinger semigroups with magnetic fields, Rev. Math. Phys. 12 (2000) 181-255. | MR 1756112 | Zbl 0961.81006

[5] R. Carmona, Pointwise bounds for Schrödinger eigenstates, Comm. Math. Phys. 62 (1978) 97-106. | MR 505706 | Zbl 0403.47016

[6] Ph. Courrège, P. Renouard, Oscillateurs anharmoniques, mesures quasi-invariantes sur C(R,R) et théorie quantique des champs en dimension 1, Astérisque (1975) 22-23. | Zbl 0316.60009

[7] J.T. Cox, On one-dimensional diffusions with time parameter set (−∞,∞), Ann. Probab. 5 (1977) 807-813. | Zbl 0376.60078

[8] E.B. Davies, B. Simon, Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians, J. Funct. Anal. 59 (1984) 335-395. | MR 766493 | Zbl 0568.47034

[9] H.-O. Georgii, Gibbs Measures and Phase Transitions, de Gruyter, Berlin, 1988. | MR 956646 | Zbl 0657.60122

[10] Y. Hariya, A new approach to construct Gibbs measures on C(R, Rd), Preprint, 2001.

[11] K. Iwata, Reversible measures of a P(φ)1 time evolution, Probabilistic Methods in Mathematical Physics, Proc. Taniguchi Symp., Katata-Kyoto, Academic Press, pp. 195-209. | Zbl 0654.60101

[12] J. Lőrinczi, R.A. Minlos, Gibbs measures for Brownian paths under the effect of an external and a small pair potential, J. Stat. Phys. 105 (2001) 607-649. | MR 1871659 | Zbl 01711031

[13] J. Lőrinczi, R.A. Minlos, H. Spohn, The infrared behavior in Nelson's model of a quantum particle coupled to a massless scalar field, Ann. Henri Poincaré 3 (2002) 1-28. | MR 1914143 | Zbl 01802458

[14] J. Lőrinczi, R.A. Minlos, H. Spohn, Infrared regular representation of the three dimensional massless Nelson model, Lett. Math. Phys. 59 (2002) 189-198. | MR 1904098 | Zbl 0996.82003

[15] H. Osada, H. Spohn, Gibbs measures relative to Brownian motion, Ann. Probab. 27 (1999) 1183-1207. | MR 1733145 | Zbl 0965.60095

[16] M. Reed, B. Simon, Methods of Modern Mathematical Physics, Vol. 4, Analysis of Operators, Academic Press, London, 1978. | MR 493421 | Zbl 0401.47001

[17] S. Roelly, H. Zessin, Sur la mécanique statistique d'une particule brownienne sur le tore, in: Séminaire de Probabilités XXV, Lecture Notes in Math., 1485, Springer, 1991, pp. 291-310. | Numdam | MR 1187787 | Zbl 0747.60100

[18] G. Royer, Unicité de certaines mesures quasi-invariantes sur C(R), Ann. Scient. École Normale Sup. Serie 4 8 (1975) 319-338. | Numdam | MR 390161 | Zbl 0351.60004

[19] G. Royer, M. Yor, Représentation intégrale de certaines mesures quasi-invariantes sur C(R) ; mesures extrémales et propriété de Markov, Ann. Inst. Fourier (Grenoble) 26 (2) (1976) 7-24. | Numdam | MR 447517 | Zbl 0295.28025

[20] B. Simon, Functional Integration and Quantum Physics, Academic Press, New York, 1979. | MR 544188 | Zbl 0434.28013

[21] B. Simon, Schrödinger semigroups, Bull. Amer. Math. Soc. 7 (1982) 447-526. | MR 670130 | Zbl 0524.35002