F. Götze

activity

19992026

most citedThe circular law for random matrices

112 citations · 441 across the 71 of their papers we have counts for

collaborators

Showing 2011 · math.PRShow all

9 papers · 2 filters

math.PR2011★ 6 cited

Rate of Convergence in the entropic free CLT

G. P. Chistyakov, F. Götze

We prove an expansion for densities in the free CLT and apply this result to an expansion in the entropic free central limit theorem assuming a moment condition of order 8 for the…

math.PR2011★ 4 cited

Characterization problems for linear forms with free summands

G. P. Chistyakov, F. Götze

Let $T_{1}, ..., T_{n}$ denote free random variables. For two linear forms $L_{1} = \sum_{j = 1}^{n} a_{j} T_{j}$ and $L_{2} = \sum_{j = 1}^{n} b_{j} T_{j}$ with real coefficients $a_{j}$ and $b_{j}$ we shall describ…

math.PR2011★ 14 cited

On the Rate of Convergence to the Marchenko--Pastur Distribution

F. Götze, A. Tikhomirov

Let $X = (X_{j k})$ denote $n \times p$ random matrix with entries $X_{j k}$ , which are independent for $1 \leq j \leq n, 1 \leq k \leq p$ . We consider the rate of convergence of empiric…

math.PR2011★ 1 cited

Asymptotic Expansions in the CLT in Free Probability

G. P. Chistyakov, F. Götze

We prove Edgeworth type expansions for distribution functions of sums of free random variables under minimal moment conditions. The proofs are based on the analytic definition of f…

math.PR2011

On the rate of convergence to the semi-circular law

Friedrich Götze, Alexander Tikhomirov

Let $X = (X_{j k})$ denote a Hermitian random matrix with entries $X_{j k}$ , which are independent for $1 \leq j \leq k$ . We consider the rate of convergence of the empirical spect…

math.PR2011★ 2 cited

Berry-Esseen bounds in the entropic central limit theorem

Sergey G. Bobkov, Gennadiy P. Chistyakov, Friedrich Götze

Berry-Esseen-type bounds for total variation and relative entropy distances to the normal law are established for the sums of non-i.i.d. random variables.

math.PR2011

Non-Uniform Bounds in Local Limit Theorems in Case of Fractional Moments

S. G. Bobkov, G. P. Chistyakov, F. Götze

Edgeworth-type expansions for convolutions of probability densities and powers of the characteristic functions with non-uniform error terms are established for i.i.d. random variab…

math.PR2011★ 65 cited

Rate of convergence and Edgeworth-type expansion in the entropic central limit theorem

Sergey G. Bobkov, Gennadiy P. Chistyakov, Friedrich Götze

An Edgeworth-type expansion is established for the entropy distance to the class of normal distributions of sums of i.i.d. random variables or vectors, satisfying minimal moment co…

math.PR2011★ 27 cited

Explicit rates of approximation in the CLT for quadratic forms

Friedrich Götze, Andrei Yu. Zaitsev

Let $X, X_{1}, X_{2}, \dots$ be i.i.d. $R^{d}$ -valued real random vectors. Assume that $E X = 0$ , $cov X = C$ , $E ∥ X ∥^{2} = σ^{2}$ and t…