A different construction of gaussian fields from Markov chains : Dirichlet covariances

Persi Diaconis; Steven N. Evans

Annales de l'I.H.P. Probabilités et statistiques (2002)

  • Volume: 38, Issue: 6, page 863-878
  • ISSN: 0246-0203

How to cite


Diaconis, Persi, and Evans, Steven N.. "A different construction of gaussian fields from Markov chains : Dirichlet covariances." Annales de l'I.H.P. Probabilités et statistiques 38.6 (2002): 863-878. <http://eudml.org/doc/77745>.

author = {Diaconis, Persi, Evans, Steven N.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Gaussian random field; Markov chains; negative correlation; Dirichlet form; potential theory},
language = {eng},
number = {6},
pages = {863-878},
publisher = {Elsevier},
title = {A different construction of gaussian fields from Markov chains : Dirichlet covariances},
url = {http://eudml.org/doc/77745},
volume = {38},
year = {2002},

AU - Diaconis, Persi
AU - Evans, Steven N.
TI - A different construction of gaussian fields from Markov chains : Dirichlet covariances
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2002
PB - Elsevier
VL - 38
IS - 6
SP - 863
EP - 878
LA - eng
KW - Gaussian random field; Markov chains; negative correlation; Dirichlet form; potential theory
UR - http://eudml.org/doc/77745
ER -


  1. [1] J. Besag, Spatial interaction and the statistical analysis of lattice systems, J. Roy. Statist. Soc. Ser. B36 (1974) 192-236, With discussion by D.R. Cox, A.G. Hawkes, P. Clifford, P. Whittle, K. Ord, R. Mead, J.M. Hammersley, and M.S. Bartlett and with a reply by the author. Zbl0327.60067MR373208
  2. [2] J. Besag, P. Green, D. Higdon, K. Mengersen, Bayesian computation and stochastic systems, Statist. Sci.10 (1) (1995) 3-66, With comments and a reply by the authors. Zbl0955.62552MR1349818
  3. [3] J. Besag, P.J. Green, Spatial statistics and Bayesian computation, J. Roy. Statist. Soc. Ser. B55 (1) (1993) 25-37. Zbl0800.62572MR1210422
  4. [4] J. Besag, D. Higdon, Bayesian analysis of agricultural field experiments, J. Roy. Statist. Soc. Ser. B Stat. Methodol.61 (4) (1999) 691-746, With discussion and a reply by the authors. Zbl0951.62091MR1722238
  5. [5] J. Besag, C. Kooperberg, On conditional and intrinsic autoregressions, Biometrika82 (4) (1995) 733-746. Zbl0899.62123MR1380811
  6. [6] A. Beurling, J. Deny, Espaces de Dirichlet. I. Le cas élémentaire, Acta Math.99 (1958) 203-224. Zbl0089.08106MR98924
  7. [7] R.N. Bhattacharya, On the functional central limit theorem and the law of the iterated logarithm for Markov processes, Z. Wahrsch. Verw. Gebiete60 (2) (1982) 185-201. Zbl0468.60034MR663900
  8. [8] E. Bolthausen, Random walk representations and entropic repulsion for gradient models. Preprint, 2001. MR1831411
  9. [9] K. Borre, Error propagation in absolute geodetic networks – a continuous approach, in: Optimization of Design and Computation of Control Networks (Proc. Internat. Sympos., Sopron, 1977), Akad. Kiadó, Budapest, 1979, pp. 459-472. 
  10. [10] K. Borre, Plane Networks and Their Applications, Birkhäuser Boston, Boston, MA, 2001. Zbl0966.65123MR1802805
  11. [11] K. Borre, P. Meissl, Strength analysis of leveling-type networks. An application of random walk theory, Geodaet. Inst. Medd.50 (1974) 80. MR475698
  12. [12] D. Brydges, J. Fröhlich, T. Spencer, The random walk representation of classical spin systems and correlation inequalities, Comm. Math. Phys.83 (1) (1982) 123-150. MR648362
  13. [13] P. Diaconis, S.N. Evans, Linear functionals of eigenvalues of random matrices, Trans. Amer. Math. Soc.353 (2001) 2615-2633. Zbl1008.15013MR1828463
  14. [14] P. Diaconis, D. Freedman, On the statistics of vision: the Julesz conjecture, J. Math. Psych.24 (2) (1981) 112-138. Zbl0494.92025MR640207
  15. [15] P. Diaconis, M. Shahshahani, On the eigenvalues of random matrices, J. Appl. Probab.31A (1994) 49-62. Zbl0807.15015MR1274717
  16. [16] M. Dozzi, Two-parameter harnesses and the Wiener process, Z. Wahrsch. Verw. Gebiete56 (4) (1981) 507-514. Zbl0456.60047MR621661
  17. [17] M. Dozzi, Stochastic Processes with a Multidimensional Parameter, Longman Scientific & Technical, Harlow, 1989. Zbl0663.60039MR991563
  18. [18] E.B. Dynkin, Markov processes and random fields, Bull. Amer. Math. Soc. (N.S.)3 (3) (1980) 975-999. Zbl0519.60046MR585179
  19. [19] E.B. Dynkin, Markov processes as a tool in field theory, J. Funct. Anal.50 (2) (1983) 167-187. Zbl0522.60078MR693227
  20. [20] E.B. Dynkin, Gaussian and non-Gaussian random fields associated with Markov processes, J. Funct. Anal.55 (3) (1984) 344-376. Zbl0533.60061MR734803
  21. [21] E.B. Dynkin, Polynomials of the occupation field and related random fields, J. Funct. Anal.58 (1) (1984) 20-52. Zbl0552.60075MR756768
  22. [22] N. Eisenbaum, Une version sans conditionnement du théorème d'isomorphisms de Dynkin, in: Séminaire de Probabilités, XXIX, Lecture Notes in Math., 1613, Springer, Berlin, 1995, pp. 266-289. Zbl0849.60075MR1459468
  23. [23] M. Fukushima, Y. Oshima, M. Takeda, Dirichlet Forms and Symmetric Markov Processes, Walter de Gruyter, Berlin, 1994. Zbl0838.31001MR1303354
  24. [24] J. Goodman, A. Sokal, Multigrid Monte–Carlo method: conceptual foundations, Phys. Rev. D40 (1989) 2035-2071. 
  25. [25] L. Gross, Hypercontractivity over complex manifolds, Acta Math.182 (2) (1999) 159-206. Zbl0983.47026MR1710181
  26. [26] J.M. Hammersley, Harnesses, in: Proc. Fifth Berkeley Sympos. Mathematical Statistics and Probability (Berkeley, Calif., 1965/66), Vol. III: Physical Sciences, Univ. California Press, Berkeley, CA, 1967, pp. 89-117. MR224144
  27. [27] K. Johansson, On random matrices from the compact classical groups, Ann. of Math. (2)145 (1997) 519-545. Zbl0883.60010MR1454702
  28. [28] J.F.C. Kingman, Random variables with unsymmetrical linear regressions, Math. Proc. Cambridge Philos. Soc.98 (2) (1985) 355-365. Zbl0574.60014MR795900
  29. [29] J.F.C. Kingman, The construction of infinite collections of random variables with linear regressions, Adv. Appl. Probab. (suppl.) (1986) 73-85. Zbl0616.60005MR868509
  30. [30] M.B. Marcus, J. Rosen, Moduli of continuity of local times of strongly symmetric Markov processes via Gaussian processes, J. Theoret. Probab.5 (4) (1992) 791-825. Zbl0761.60035MR1182681
  31. [31] M.B. Marcus, J. Rosen, Moment generating functions for local times of symmetric Markov processes and random walks, in: Probability in Banach Spaces, 8 (Brunswick, ME, 1991), Birkhäuser Boston, Boston, MA, 1992, pp. 364-376. Zbl0788.60092MR1227631
  32. [32] M.B. Marcus, J. Rosen, p-variation of the local times of symmetric stable processes and of Gaussian processes with stationary increments, Ann. Probab.20 (4) (1992) 1685-1713. Zbl0762.60069MR1188038
  33. [33] M.B. Marcus, J. Rosen, Sample path properties of the local times of strongly symmetric Markov processes via Gaussian processes, Ann. Probab.20 (4) (1992) 1603-1684. Zbl0762.60068MR1188037
  34. [34] M.B. Marcus, J. Rosen, φ-variation of the local times of symmetric Lévy processes and stationary Gaussian processes, in: Seminar on Stochastic Processes, 1992 (Seattle, WA, 1992), Birkhäuser Boston, Boston, MA, 1993, pp. 209-220. Zbl0793.60043
  35. [35] M.L. Mehta, Random Matrices, Academic Press, Boston, MA, 1991. Zbl0780.60014MR1083764
  36. [36] H.-J. Schmeisser, H. Triebel, Topics in Fourier Analysis and Function Spaces, Wiley, Chichester, 1987. Zbl0661.46025MR891189
  37. [37] P. Sheppard, On the Ray-Knight Markov property of local times, J. London Math. Soc. (2)31 (2) (1985) 377-384. Zbl0535.60070MR809960
  38. [38] K. Symanzik, Euclidean quantum field theory, in: Jost R. (Ed.), Local Quantum Theory, Academic, New York, 1969. 
  39. [39] D. Williams, Some basic theorems on harnesses, in: Stochastic Analysis (a tribute to the memory of Rollo Davidson), Wiley, London, 1973, pp. 349-363. MR362565
  40. [40] D. Ylvisaker, Prediction and design, Ann. Statist.15 (1) (1987) 1-19. Zbl0646.62080MR885721

NotesEmbed ?


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.