|
Dynamic approach to a stochastic domination: The FKG and Brascamp-Lieb inequalities
Author(s):
Tadahisa
Funaki;
Kou
Toukairin
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1915-1922.
MSC (2000):
Primary 82B31;
Secondary 82B20, 60K35
Posted:
February 6, 2007
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
A coupling based on a pair of stochastic differential equations is introduced to show a stochastic domination for a system with continuous spins, from which the FKG and Brascamp-Lieb like inequalities follow.
References:
-
- 1.
- L. AMBROSIO, G. BUTTAZZO, L.A. CAFFARELLI, C. VILLANI AND Y. BRENIER, Optimal transportation and applications, Martina Franca, Italy 2001, edited by L.A. Caffarelli and S. Salsa, Lecture Notes in Math., 1813 (2003). MR 2006302 (2004m:49007)
- 2.
- D. BAKRY AND D. MICHEL, Sur les inégalités FKG, Séminaire de Probabilités, XXVI, pp. 170-188, Lecture Notes in Math., 1526 (1992). MR 1231994 (94k:60025)
- 3.
- H.J. BRASCAMP AND E.H. LIEB, On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation, J. Funct. Anal., 22 (1976), pp. 366-389. MR 0450480 (56:8774)
- 4.
- L.A. CAFFARELLI, Monotonicity properties of optimal transportation and the FKG and related inequalities, Commun. Math. Phys., 214 (2000), pp. 547-563; Erratum, Commun. Math. Phys., 225 (2002), pp. 449-450. MR 1800860 (2002c:60029) MR 1889232 (2003b:60031)
- 5.
- G. DA PRATO AND J. ZABCZYK, Ergodicity for infinite dimensional systems, London Math. Soc. Lect. Note Series, 229, Cambridge Univ. Press, 1996. MR 1417491 (97k:60165)
- 6.
- C.M. FORTUIN, P.W. KASTELEYN, J. GINIBRE, Correlation inequalities on some partially ordered sets, Commun. Math. Phys., 22 (1971), pp. 90-103. MR 0309498 (46:8607)
- 7.
- G. GIACOMIN, On stochastic domination in the Brascamp-Lieb framework, Math. Proc. Cambridge Philos. Soc., 134 (2003), pp. 507-514. MR 1981215 (2004d:60045)
- 8.
- Y. HARIYA, private communication, 2005, Oct.
- 9.
- R. HOLLEY, Remarks on the FKG inequalities, Commun. Math. Phys., 36 (1974), pp. 227-231. MR 0341552 (49:6300)
- 10.
- K. ICHIHARA AND H. KUNITA, A classification of the second order degenerate elliptic operators and its probabilistic characterization, Z. Wahr. verw. Geb., 30 (1974), pp. 235-254; Supplements and corrections, Z. Wahr. verw. Geb., 39 (1977), pp. 81-84. MR 0381007 (52:1904) MR 0488328 (58:7877)
- 11.
- N. IKEDA AND S. WATANABE, Stochastic differential equations and diffusion processes, 2nd edition, North-Holland, Amsterdam (Kodansha Ltd., Tokyo), 1989. MR 1011252 (90m:60069)
- 12.
- T.M. LIGGETT, Interacting Particle Systems, Springer, 1985. MR 0776231 (86e:60089)
- 13.
- C.J. PRESTON, A generalization of the FKG inequalities, Commun. Math. Phys., 36 (1974), pp. 233-241. MR 0341553 (49:6301)
- 14.
- D.W. STROOCK, Probability theory, an analytic view, Cambridge Univ. Press, 1993. MR 1267569 (95f:60003)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
82B31,
82B20, 60K35
Retrieve articles in all Journals with MSC
(2000):
82B31,
82B20, 60K35
Additional Information:
Tadahisa
Funaki
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Tokyo 153-8914, Japan
Email:
funaki@ms.u-tokyo.ac.jp
Kou
Toukairin
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Tokyo 153-8914, Japan
Address at time of publication:
Lehman Brothers Japan Inc., Roppongi Hills, Tokyo
Email:
kou.toukairin@lehman.com
DOI:
10.1090/S0002-9939-07-08757-6
PII:
S 0002-9939(07)08757-6
Keywords:
Stochastic domination,
FKG inequality,
Brascamp-Lieb inequality,
Coupling
Received by editor(s):
April 10, 2006
Posted:
February 6, 2007
Additional Notes:
The first author was supported in part by JSPS Grants (B)14340029 and 17654020
Communicated by:
Edward C. Waymire
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org