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Limit theorems for skew translations
| 1. | School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom |
References:
| [1] |
A. Bufetov, Limit theorems for translation flows, Ann. of Math. (2), 179 (2014), 431-499.
doi: 10.4007/annals.2014.179.2.2. |
| [2] |
A. Bufetov and G. Forni, Limit theorems for horocycle flows,, , ().
|
| [3] |
A. Bufetov and B. Solomyak, Limit theorems for self-similar tilings, Comm. Math. Phys., 319 (2013), 761-789.
doi: 10.1007/s00220-012-1624-7. |
| [4] |
D. Dolgopyat and B. Fayad, Deviations of ergodic sums for toral translations I. Convex bodies, Geom. Funct. Anal., 24 (2014), 85-115.
doi: 10.1007/s00039-014-0254-y. |
| [5] |
D. Dolgopyat and B. Fayad, Deviations of ergodic sums for toral translations II. Boxes,, , ().
|
| [6] |
F. Cellarosi, Limiting curlicue measures for theta sums, Ann. Inst. Henri Poincaré Probab. Stat., 47 (2011), 466-497.
doi: 10.1214/10-AIHP361. |
| [7] |
A. Fedotov and F. Klopp, An exact renormalization formula for Gaussian exponential sums and applications, Amer. J. Math., 134 (2012), 711-748.
doi: 10.1353/ajm.2012.0016. |
| [8] |
L. Flaminio and G. Forni, Equidistribution of nilflows and applications to theta sums, Ergodic Theory Dynam. Systems, 26 (2006), 409-433.
doi: 10.1017/S014338570500060X. |
| [9] |
W. B. Jurkat and J. W. Van Horne, The proof of the central limit theorem for theta sums, Duke Math. J., 48 (1981), 873-885.
doi: 10.1215/S0012-7094-81-04848-1. |
| [10] |
W. B. Jurkat and J. W. Van Horne, On the central limit theorem for theta series, Michigan Math. J., 29 (1982), 65-77.
doi: 10.1307/mmj/1029002615. |
| [11] |
W. B. Jurkat and J. W. Van Horne, The uniform central limit theorem for theta sums, Duke Math. J., 50 (1983), 649-666.
doi: 10.1215/S0012-7094-83-05030-5. |
| [12] |
H. Kesten, Uniform distribution mod 1, Ann. of Math. (2), 71 (1960), 445-471.
doi: 10.2307/1969938. |
| [13] |
H. Kesten, Uniform distribution mod 1. II,, Acta Arith., 7 (): 355.
|
| [14] |
J. Marklof, Limit theorems for theta sums, Duke Math. J., 97 (1999), 127-153.
doi: 10.1215/S0012-7094-99-09706-5. |
| [15] |
J. Marklof, Almost modular functions and the distribution of $n^2 x$ modulo one, Int. Math. Res. Not., 39 (2003), 2131-2151.
doi: 10.1155/S1073792803130292. |
| [16] |
J. Marklof, Pair correlation densities of inhomogeneous quadratic forms, Ann. of Math. (2), 158 (2003), 419-471.
doi: 10.4007/annals.2003.158.419. |
| [17] |
Y. G. Sinai and C. Ulcigrai, A limit theorem for Birkhoff sums of nonintegrable functions over rotations, in Geometric and Probabilistic Structures in Dynamics, Contemp. Math., 469, Amer. Math. Soc., Providence, RI, 2008, 317-340.
doi: 10.1090/conm/469/09174. |
show all references
References:
| [1] |
A. Bufetov, Limit theorems for translation flows, Ann. of Math. (2), 179 (2014), 431-499.
doi: 10.4007/annals.2014.179.2.2. |
| [2] |
A. Bufetov and G. Forni, Limit theorems for horocycle flows,, , ().
|
| [3] |
A. Bufetov and B. Solomyak, Limit theorems for self-similar tilings, Comm. Math. Phys., 319 (2013), 761-789.
doi: 10.1007/s00220-012-1624-7. |
| [4] |
D. Dolgopyat and B. Fayad, Deviations of ergodic sums for toral translations I. Convex bodies, Geom. Funct. Anal., 24 (2014), 85-115.
doi: 10.1007/s00039-014-0254-y. |
| [5] |
D. Dolgopyat and B. Fayad, Deviations of ergodic sums for toral translations II. Boxes,, , ().
|
| [6] |
F. Cellarosi, Limiting curlicue measures for theta sums, Ann. Inst. Henri Poincaré Probab. Stat., 47 (2011), 466-497.
doi: 10.1214/10-AIHP361. |
| [7] |
A. Fedotov and F. Klopp, An exact renormalization formula for Gaussian exponential sums and applications, Amer. J. Math., 134 (2012), 711-748.
doi: 10.1353/ajm.2012.0016. |
| [8] |
L. Flaminio and G. Forni, Equidistribution of nilflows and applications to theta sums, Ergodic Theory Dynam. Systems, 26 (2006), 409-433.
doi: 10.1017/S014338570500060X. |
| [9] |
W. B. Jurkat and J. W. Van Horne, The proof of the central limit theorem for theta sums, Duke Math. J., 48 (1981), 873-885.
doi: 10.1215/S0012-7094-81-04848-1. |
| [10] |
W. B. Jurkat and J. W. Van Horne, On the central limit theorem for theta series, Michigan Math. J., 29 (1982), 65-77.
doi: 10.1307/mmj/1029002615. |
| [11] |
W. B. Jurkat and J. W. Van Horne, The uniform central limit theorem for theta sums, Duke Math. J., 50 (1983), 649-666.
doi: 10.1215/S0012-7094-83-05030-5. |
| [12] |
H. Kesten, Uniform distribution mod 1, Ann. of Math. (2), 71 (1960), 445-471.
doi: 10.2307/1969938. |
| [13] |
H. Kesten, Uniform distribution mod 1. II,, Acta Arith., 7 (): 355.
|
| [14] |
J. Marklof, Limit theorems for theta sums, Duke Math. J., 97 (1999), 127-153.
doi: 10.1215/S0012-7094-99-09706-5. |
| [15] |
J. Marklof, Almost modular functions and the distribution of $n^2 x$ modulo one, Int. Math. Res. Not., 39 (2003), 2131-2151.
doi: 10.1155/S1073792803130292. |
| [16] |
J. Marklof, Pair correlation densities of inhomogeneous quadratic forms, Ann. of Math. (2), 158 (2003), 419-471.
doi: 10.4007/annals.2003.158.419. |
| [17] |
Y. G. Sinai and C. Ulcigrai, A limit theorem for Birkhoff sums of nonintegrable functions over rotations, in Geometric and Probabilistic Structures in Dynamics, Contemp. Math., 469, Amer. Math. Soc., Providence, RI, 2008, 317-340.
doi: 10.1090/conm/469/09174. |
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