Uniqueness of Gibbs measures relative to brownian motion
Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 5, pp. 877-889. 
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     author = {Betz, Volker and L\H{o}rinczi, J\'ozsef},
     title = {Uniqueness of {Gibbs} measures relative to brownian motion},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {877--889},
     publisher = {Elsevier},
     volume = {39},
     number = {5},
     year = {2003},
     doi = {10.1016/S0246-0203(03)00021-9},
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     zbl = {1025.60043},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/S0246-0203(03)00021-9/}
}
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Betz, Volker; Lőrinczi, József. Uniqueness of Gibbs measures relative to brownian motion. Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 5, pp. 877-889. doi : 10.1016/S0246-0203(03)00021-9. http://www.numdam.org/articles/10.1016/S0246-0203(03)00021-9/

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

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

[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

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

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

[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. | Numdam | Zbl

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

[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 | Zbl

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

[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

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

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

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