Uniqueness of Gibbs measures relative to brownian motion

Volker Betz; József Lőrinczi

Annales de l'I.H.P. Probabilités et statistiques (2003)

  • Volume: 39, Issue: 5, page 877-889
  • ISSN: 0246-0203

How to cite

top

Betz, Volker, and Lőrinczi, József. "Uniqueness of Gibbs measures relative to brownian motion." Annales de l'I.H.P. Probabilités et statistiques 39.5 (2003): 877-889. <http://eudml.org/doc/77784>.

@article{Betz2003,
author = {Betz, Volker, Lőrinczi, József},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Gibbs measure; diffusion process; Brownian motion},
language = {eng},
number = {5},
pages = {877-889},
publisher = {Elsevier},
title = {Uniqueness of Gibbs measures relative to brownian motion},
url = {http://eudml.org/doc/77784},
volume = {39},
year = {2003},
}

TY - JOUR
AU - Betz, Volker
AU - Lőrinczi, József
TI - Uniqueness of Gibbs measures relative to brownian motion
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2003
PB - Elsevier
VL - 39
IS - 5
SP - 877
EP - 889
LA - eng
KW - Gibbs measure; diffusion process; Brownian motion
UR - http://eudml.org/doc/77784
ER -

References

top
  1. [1] G. Benfatto, E. Presutti, M. Pulvirenti, DLR Measures for one-dimensional harmonic systems, Z. Wahr. Geb.41 (1978) 305-312. Zbl0355.60063MR467969
  2. [2] V. Betz, Existence of Gibbs measures relative to Brownian motion, Markov Proc. Related Fields1 (2002) 1-1, To appear. Zbl1017.60041MR1973322
  3. [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. Zbl1029.81022
  4. [4] K. Broderix, D. Hundertmark, H. Leschke, Continuity properties of Schrödinger semigroups with magnetic fields, Rev. Math. Phys.12 (2000) 181-255. Zbl0961.81006MR1756112
  5. [5] R. Carmona, Pointwise bounds for Schrödinger eigenstates, Comm. Math. Phys.62 (1978) 97-106. Zbl0403.47016MR505706
  6. [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. Zbl0316.60009
  7. [7] J.T. Cox, On one-dimensional diffusions with time parameter set (−∞,∞), Ann. Probab.5 (1977) 807-813. Zbl0376.60078
  8. [8] E.B. Davies, B. Simon, Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians, J. Funct. Anal.59 (1984) 335-395. Zbl0568.47034MR766493
  9. [9] H.-O. Georgii, Gibbs Measures and Phase Transitions, de Gruyter, Berlin, 1988. Zbl0657.60122MR956646
  10. [10] Y. Hariya, A new approach to construct Gibbs measures on C(R, Rd), Preprint, 2001. 
  11. [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. Zbl0654.60101
  12. [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. Zbl1174.81325MR1871659
  13. [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 Poincaré3 (2002) 1-28. Zbl1172.81330MR1914143
  14. [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. Zbl0996.82003MR1904098
  15. [15] H. Osada, H. Spohn, Gibbs measures relative to Brownian motion, Ann. Probab.27 (1999) 1183-1207. Zbl0965.60095MR1733145
  16. [16] M. Reed, B. Simon, Methods of Modern Mathematical Physics, Vol. 4, Analysis of Operators, Academic Press, London, 1978. Zbl0401.47001MR493421
  17. [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. Zbl0747.60100MR1187787
  18. [18] G. Royer, Unicité de certaines mesures quasi-invariantes sur C(R), Ann. Scient. École Normale Sup. Serie 48 (1975) 319-338. Zbl0351.60004MR390161
  19. [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. Zbl0295.28025MR447517
  20. [20] B. Simon, Functional Integration and Quantum Physics, Academic Press, New York, 1979. Zbl0434.28013MR544188
  21. [21] B. Simon, Schrödinger semigroups, Bull. Amer. Math. Soc.7 (1982) 447-526. Zbl0524.35002MR670130

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.