PUBLICATIONS OF PÉTER MAJOR

The pdf file of these works can be obtained by clicking to the word article after the title. In the case of the works with number 34 or greater both the Tex, dvi and pdf can be obtained in such a way.


To papers submitted for publication (together with their TeX, dvi and pdf files.)


62. 
Non-central limit theorem for non-linear functionals of vector valued Gaussian stationary random fields. submitted to Annals of Probability (2023) The article
61. 
Wiener--Ito integral representation in vector valued Gaussion stationary random fields. Part II. submitted to Moscow Mathematical Journals (2023) The article
60. 
Wiener--Ito integral representation in vector valued Gaussion stationary random fields. Part I. Moscow Mathematical Journals (2020) Volume 20, Number 4. Pages 749--812 Special Volume dedicated for the 90-th birthday of R. L. Dobrushin The article
59. 
A Thouless-like effect in the Dyson hierarchical model with continuous symmetry.
Pure and Applied Functional Analysis (2021) Volume 6, Number 1, Pages 101-175 Special Volume dedicated for the 85.-th birthday of Ya. G. Sinai The article
58. 
Sharp tail distribution estimates for the supremum of a class of sums of i.i.d. random variables. Stochastic processes and their applications (2016)
Volume 126 118--137 The article

Here is a 5 minutes long audioslide about this work.
Here is the text of a (possible) longer conference talk about this paper.


57. 
Sharp estimate on the supremum of a class of sums of small i.i.d. random variables. Stochastic processes and their applications (2016)
Volume 126 100--117 The article

Here is a 5 minutes long audioslide about this work.
Here is the text of a (possible) longer conference talk about this paper.

56. 
Multiple Wiener--Ito integrals with applications to limit theorems. Lecture Notes in Mathematics 849 Second edition. Revised version , Springer Verlag, Berlin--Heidelberg--New York, 2014 The article
55. 
On the estimation of multiple random integrals and degenerate U-statistics. 2079, Lecture Notes in Mathematics, Springer Verlag, Berlin--Heidelberg--New York, 2013 The article
54. 
Estimation of multiple random integrals and U-statistics. Moscow Mathematical Journals Volume 10 no. 4 (2010) (747-763) The article
53. 
On a multivariate version of Bernstein's inequality. Electronic Journal of Probability Volume 12 (2007) (996--988) The article
52. 
A multivariate generalization of Hoeffding's inequality. Electronic Communication in Probability Volume 2 (2006) (220--229) The article
51. 
Tail behaviour of multiple random integrals and $U$-statistics. Probability Reviews series Volume 2 (2005) (448-505) The article
50. 
An estimate on the supremum of a nice class of stochastic integrals and U-statistics. Probability Theory and Related Fields 134 (3) (2006) (489-537) The article
49. 
An estimate about multiple stochastic integrals with respect to a normalized empirical measure. Studia Scientarum Mathematicarum Hungarica 42 No. 3 (2005) (295-341) The article
48. 
Limit theorems on the direct product of a non-compact Lie group and a compact group. (with Gyula Pap) Studia Scientarum Mathematicarum Hungarica 38 No. 1--2 (2001) 279--297 The article
47. 
Almost sure functional limit theorems. Part II. The case of independent random variables. Studia Scientarum Mathematicarum Hungarica 36 No. 1--2 (2000) 231--273 The article
46. 
Almost sure functional limit theorems. Part I. The general case. Studia Scientarum Mathematicarum Hungarica 34 (1998) 273--304 The article
45. 
The limit behaviour of elementary symmetric polynomials of i.i.d. random variables when their order tends to infinity. The Annals of Probability 27 No. 4 (1999) 1980--2010 The article
44. 
A note on nonparametric estimations. in: Asymptotic Methods in Probability and Statistics A volume in Honour of Miklós Csörgõ. North--Holland (1998) 759--774 (with L. Rejtõ) The article
43. 
A counter-example in ergodic theory. Acta Sci. Math. (Szeged) 62 (1996) 247--258 The article
42. 
Limit theorems about the distribution of almost periodic functions. Studia Scientarum Mathematicarum Hungarica 31 (1996) 203--224 The article
41. 
Asymptotic distributions for weighted U-statistics. The Annals of Probability 22 (1994) 1514--1535 The article
40. 
On the number of lattice points between two enlarged and randomly shifted copies of an oval. Probab. Th. Rel. Fields 100 (1994) 253--268 with Zh.Cheng and J.L. Lebowitz The article
39. 
Poisson law for the number of lattice points in a random strip with finite area. Probab. Th. Rel. Fields 92 (1992) 423--464 The article
38. 
Phase-transition in statistical physical models with discrete and continuous symmetries. In IMA volume New Directions in Time Series (with P.M. Bleher) The article
37. 
Renormalization of Dyson's vector-valued hierarchical model at low temperatures. Probability Theory and Mathematical Statistics Ed. B. Grigelionis et al. , 1990, VSP/Mokulas (with P.M. Bleher) The article
36. 
A note on the approximation of the uniform empirical process. Annals of Probability 18 (1990) 129--139 The article
35. 
The large-scale limit of Dyson's hierarchical vector-valued model at low temperatures. The marginal case c=sqrt 2. Comm. Math. Physics 125 (1989), 43--69 (with P.M.Bleher) The article
34. 
The large-scale limit of Dyson's hierarchical model at low temperatures. The non-Gaussian case. Part II. Annales de l'Institut Henri Poincaré, Série Physique Théorique, Volume 49 fascicule 1 (1988), 86--143 (with P.M. Bleher) The article
33. 
The large-scale limit of Dyson's hierarchical vector-valued model at low temperatures. The non-Gaussian case. Part I. Annales de l'Institut Henri Poincaré, Série Physique Théorique, Volume 49 fascicule 1 (1988), 1--85 (with P.M. Bleher) The article
32. 
Strong embedding of estimation of the distribution function under random censorship. Ann. Stat. 16 (1988), 1113--1132 (with L. Rejtõ) The article
31. 
On the tail behaviour of the distribution function of multiple stochastic integrals. Probab. Th. Rel. Fields 78 (1988), 419--435 The article
30. 
On the set visited once by a random walk. Probab. Th. Rel. Fields 77 (1988), 117--128 The article
29. 
Limit theorems in statistical Physics; on Dyson's hierarchical model. Proceedings of the First World Congress of the Bernoulli Society. Ed. by Yu. V. Prohorov et al., VSP, Utrecht (with P.M. Bleher) The article
28. 
Critical phenomena and universal exponents in statistical physics. On Dyson's hierarchical model. Annals of Probability 15 1987, 431--477 (Special invited paper, with P.M. Bleher) The article
27. 
Renormalization of Dyson's hierarchical vector valued varphi^4 model at low temperatures. Comm. Math. Physics 95 (1984), 487--532 (with P.M. Bleher) The article
26. 
Central limit theorems for non-linear functionals of Gaussian fields. Journal of Multivariate Analysis 13 (1983), 425--441 (with P. Breuer) The article
25. 
On renormalizing Gaussian fields. Z. Wahrscheinlichkeitstheorie verw. Gebiete 59 (1982), 515--533 The article
24. 
On a class of self-similar fields. Sel. Mat. Sov. Vol. 1, No. 3 (1981), 293--302 The article
23. 
On the asymptotical behaviour of some self-similar random fields. Sel. Mat. Sov. Vol. 1, No.3 (1981), 265--291 (with R.L. Dobrushin) The article
22. 
Multiple Wiener--Ito Integrals. Lecture Notes in Mathematics 849, Springer Verlag, Berlin--Heidelberg--New York, 1981. The article
21. 
Renormalizing the voter model. Space and space-time renormalization. Studia Sci. Math. Hungar. 15 (1980), 321--341 The article
20. 
Limit theorems for non-linear functionals of Gaussian sequences. Z.Wahrscheinlichkeitstheorie und verw. Gebiete 57 (1981), 129--158 The article
19. 
On the effect of collisions on the motion of an atom in R^1. Annals of Probability 8 (1980), 1068--1078 (with D. Szász) The article
18. 
A local limit theorem for the convolution of probability measures on a compact connected group. Z. Wahrscheinlichkeitstheorie und verw. Gebiete 50 (1979) 137--148 (with S.B. Shlosman) The article
17. 
Non-central limit theorems for non-linear functionals of Gaussian fields. Z. Wahrscheinlichkeitstheorie verw. Gebiete 50 (1979), 27--52 (with R.L. Dobrushin). The article
16. 
An improvement of Strassen's invariance principle. The Annals of Probability 7 (1979), 55--60 The article
15. 
On the invariance principle for sums of independent identically distributed random variables. Journal of Multivariate Analysis 8 (1978), 487--517 The article
14. 
A note on Kolmogorov's law of iterated logarithm. Studia Sci. Math. Hungar. 12 (1977), 161--167 The article
13. 
Reconstructing the distribution from partial sums of samples. The Annals of Probability 5 (1977), (with G. Halász) The article
12. 
The approximation of partial sums of i.i.r.v.s when the summands have only two moments. Z. Wahrscheinlichkeitstheorie verw. Gebiete 35 (1976), 221--229 The article
11. 
The approximation of partial sums of independent R.V.-s. Z. Wahrscheinlichkeitstheorie verw. Gebiete 35 (1976), 213--220. The article
10. 
Letter to the editors. (in Russian) Theory of Probability and its applications 20 (1975), 219--220 (with D. Szász) The article
9. 
An approximation of partial sums of independent RV's and the sample DF. II. Z. Wahrscheinlichkeitstheorie und verw. Gebiete 34 (1976), 33--58 (with J. Komlós and G. Tusnády) The article
8. 
An approximation of partial sums of independent RV's and the sample DF. I. Z. Wahrscheinlichkeitstheorie und verw. Gebiete 32 (1975), 111--131 (with J. Komlós and G. Tusnády) The article
7. 
On the empirical process when parameters are estimated. European Meeting of Statisticians, Prague (1974), 87--97 (with M. Csörgõ, J. Komlós, P. Révész and G. Tusnády) The article
6. 
Weak convergence and embedding. Coll. Math. Soc. J. Bolyai 11 Limit Theorems of Probablity Theory. Keszthely (1974), 149--165 (with J. Komlós, and G. Tusnády) The article
5. 
On testing normality. (in Hungarian). MTA III. Osztály Közleményei 22 (1973), 257--291 (with G. Tusnády) The article
4. 
A limit theorem for the Robbins--Monro approximation. Z. Wahrscheinlichkeitstheorie verw. Gebiete 27 (1973), 79--86 (with P. Révész) The article
3. 
On a non-parametric estimation of the regression function. Studia Sci. Math. Hungar. 8 (1973), 347--361 The article
2. 
A note to a paper of Dudley. Studia Sci. Math. Hungar. 8 (1973), 151--152 (with L. Lovász) The article
1. 
A law of the iterated logarithm for the Robbins--Monro method. Studia Sci. Math. Hungar. 8 (1973), 95--102 The article



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