01.01.05 (Probability theory and mathematical statistics)
Birth date:
10.08.1951
E-mail:
Keywords:
strong mixing condition,
Central Limit Theorems,
Random Matrices,
Semi-circular Law,
Circular Law.
Subject:
Limit Theorems of Probability Theory
Main publications:
Tikhomirov A. N., “Skorost skhodimosti v tsentralnoi predelnoi teoreme dlya slabo zavisimykh velichin.”, Teoriya veroyatnostei i ee primeneniya, 25:4 (1980), 800-818
Goetze F. and Tikhomirov A. N., “The rate of convergence for spectra of GUE and LUE matrix ensembles”, Central European Journal of Mathematics, 3:4 (2005), 666-704
Goetze F. and Tikhomirov A. N., “Asymptotic distributions of quadratic forms”, Annals of Probability, 27:2 (1999), 1072–1098
Goetze F. and Tikhomirov A. N., “The circular law for random matrices”, Annals of Probability, 38:4 (2010), 1444–1491
Goetze F., Tikhomirov A. N., “Rate of convergence to the semi-circular law”, Probability Theory and Related Fields, 127:2 (2003), 228–276
A. N. Tihomirov, “On the rate of convergence in the central limit theorem for weakly dependent random variables”, Theory Probab. Appl., 25:4 (1981), 790–809
2.
F. Götze, A. N. Tikhomirov, “The circular law for random matrices”, Ann. Probab, 38:4 (2010), 1444–1491
N. V. Alexeev, F. Götze, A. N. Tikhomirov, “Asymptotic distribution of singular values of powers of random matrices”, Lith. Math. J., 50:2 (2010), 121–-132
F. Götze, A. A. Naumov, A. N. Tikhomirov, “Limit theorems for two classes of random matrices with dependent entries”, Theory Probab. Appl., 59:1 (2015), 23–39
10.
Theory Probab. Appl., 51:1 (2007), 42–64
11.
S. G. Bobkov, F. Götze, A. N. Tikhomirov, “On concentration of empirical measures and convergence to the semi-circle law”, J. Theoret. Probab., 23:3 (2010), 792–823
A. N. Tikhomirov, “On the accuracy of the normal approximation of the probability of sums of weakly dependent Hilbert-space-valued random variables hitting a ball. I”, Theory Probab. Appl., 36:4 (1991), 738–751
17.
F. Götze, A. A. Naumov, A. N. Tikhomirov, “Local semicircle law under moment conditions: Stieltjes transform, rigidity and delocalization”, Theory Probab. Appl., 62:1 (2018), 58–83
18.
D. A. Timushev, A. N. Tikhomirov, A. A. Kholopov, “Rate of convergence to the semicircle law for the Gaussian orthogonal ensemble”, Theory Probab. Appl., 52:1 (2008), 171–177
19.
A. N. Tikhomirov, “On asymptotics for the spectrum of the product of two random rectangular matrices”, Siberian Math. J., 52:4 (2011), 747–762
20.
J. Math. Sci. (N. Y.), 147:4 (2007), 6891–6911
21.
F. Götze, A. N. Tikhomirov, “Asymptotic expansions in non-central limit theorems for quadratic forms.”, J. Theoret. Probab., 18:4 (2005), 757–-811
F. Götze, A. A. Naumov, A. N. Tikhomirov, “Moment Inequalities for Linear and Nonlinear Statistics”, Theory Probab. Appl., 65:1 (2020), 1–16
23.
F. Götze, D. A. Timushev, A. N. Tikhomirov, “Rate of convergence to the semi-circle law for the deformed Gaussian unitary ensemble.”, Cent. Eur. J. Math., 5:2 (2007), 305–-334
A. N. Tihomirov, “On the distribution of the maximal sum of weakly dependent random variables”, Theory Probab. Appl., 31:4 (1986), 733–738
25.
A. N. Tikhomirov, “Asymptotic distribution of singular values for matrices in a spherical ensemble”, Siberian Adv. Math., 24:4 (2014), 282–303
26.
N. Alexeev, F. Götze, A. Tikhomirov, “On the asymptotic distribution of the singular values of powers of random matrices”, J. Math. Sci. (N. Y.), 199:2 (2014), 68–87
27.
A. N. Tikhomirov, “The rate of convergence of the expected spectral distribution function of a sample covariance matrix to the Marchenko-Pastur distribution.”, Siberian Adv. Math., 19:4 (2009), 277–286
A. N. Tikhomirov, “The rate of convergence of the expected spectral distribution function of a sample covariance matrix to the Marchenko-Pastur distribution.”, Siberian Adv. Math., 19:4 (2009), 277–-286
A. V. Nadutkina, A. N. Tikhomirov, D. A. Timushev, “Marchenko–Pastur law for the spectrum of a random weighted bipartite graph”, Siberian Adv. Math., 34:2 (2024), 146–153
30.
F. Götze, D. A. Timushev, A. N. Tikhomirov, “Local Marchenko–Pastur law for sparse rectangular random matrices”, Dokl. Math., 104:3 (2021), 332–335
31.
J. Math. Sci. (N. Y.), 163:4 (2010), 328–351
32.
A. N. Tikhomirov, “On the accuracy of normal approximation of the probability of hitting a ball of sums of weakly dependent Hilbert space valued random variables II”, Theory Probab. Appl., 38:1 (1993), 80–94
33.
A. N. Tikhomirov, “Normal approximation of sums of vector-valued mixing random fields”, Dokl. Akad. Nauk SSSR, 272:2 (1983), 312–314
34.
F. Götze, A. N. Tikhomirov, “Limit theorems for spectra of random matrices with martingale structure.”, Stein's method and applications, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap.,, 5, Singapore Univ. Press,, Singapore, 2005, 181–-193
35.
A. N. Tikhomirov, “On the rate of convergence in the CLT for sequences of weakly dependent Hilbert valued random variables”, J. Math. Sci., 75:5 (1995), 1985
36.
A. N. Tikhomirov, “On the normal approximation of sums of weakly dependent Hilbert-valued random variables.”, Probability theory and mathematical statistics. Proc. 5th Vilnius Conf. (Vilnius, 1989), 2, Mokslas, Vilnius, 1990, 482––494
37.
A. N. Tikhomirov, “Stein's method and characteristic functions”, Russian Math. Surveys, 80:4 (2025), 667–716
38.
F. Götze, A. N. Tikhomirov, D. A. Timushev, “Local laws for sparse sample covariance matrices without the truncation condition”, Veroyatnost i statistika. 32, Posvyaschaetsya yubileyu Ildara Abdullovicha IBRAGIMOVA, Zap. nauchn. sem. POMI, 510, POMI, SPb., 2022, 65–86;
Inequalities for the Moments of Quadratic Forms A. N. Tikhomirov International Scientific Conference "Probability Theory and its Applications" On Occasion of 85th Birthday of Yu. V. Prokhorov February 12, 2015 17:15
