# On almost sure convergence of the spectral distribution of a power of a random matrix to the Fuss-Catalan distribution

## Related Articles

- On the Asymptotic Distribution of Singular Values of Powers of Random Matrices. Alexeev, N.; Götze, F.; Tikhomirov, A. // Journal of Mathematical Sciences;May2014, Vol. 199 Issue 2, p68
We consider powers of random matrices with independent entries. Let X, i, j â‰¥ 1, be independent complex random variables with E X = 0 and E| X| = 1, and let X denote an n Ã— n matrix with | X| âˆ’ X for 1 â‰¤ i, j â‰¤ n. Denote by $ s_1^{(m)}\geq \ldots \geq s_n^{(m) } $ the...

- On asymptotics for the spectrum of the product of two random rectangular matrices. Tikhomirov, A. // Siberian Mathematical Journal;Jul2011, Vol. 52 Issue 4, p747
On assuming the Lindeberg condition, we prove the convergence of the expected spectral distribution of the product of two independent random rectangular matrices with independent entries to a certain distribution on the unit disk in the complex plane. We obtain an explicit expression for the...

- Localization and delocalization of eigenvectors for heavy-tailed random matrices. Bordenave, Charles; Guionnet, Alice // Probability Theory & Related Fields;Dec2013, Vol. 157 Issue 3/4, p885
Consider an $$n \times n$$ Hermitian random matrix with, above the diagonal, independent entries with $$\alpha $$ -stable symmetric distribution and $$0 < \alpha < 2$$ . We establish new bounds on the rate of convergence of the empirical spectral distribution of this random matrix as $$n$$ goes...

- Convergence of Luo and Tsai's iterative algorithm for estimation in proportional likelihood ratio models. Davidov, O.; Iliopoulos, G. // Biometrika;Sep2013, Vol. 100 Issue 3, p778
Luo & Tsai (2012, Biometrika) introduced the proportional likelihood ratio model. They proposed an iterative algorithm for the estimation of the baseline distribution function but did not establish its convergence. Here we provide a proof of convergence.

- A Class of Strong Limit Theorems for Nonhomogeneous Markov Chains Field Indexed by a Homogeneous Tree. Kangkang Wang; Decai Zong // Southeast Asian Bulletin of Mathematics;2012, Vol. 36 Issue 6, p891
In this paper, we study the strong limit theorems on the a.s. convergence for the harmonic mean of the transition probabilities of nonhomogeneous Markov chain indexed by the homogeneous tree. In the proof, we apply the tool of conditional moment generating functions and establishment of the...

- ON THE ASYMPTOTIC BEHAVIOUR OF EXTREMES AND NEAR MAXIMA OF RANDOM OBSERVATIONS FROM THE GENERAL ERROR DISTRIBUTIONS. VASUDEVA, R.; KUMARI, J. VASANTHA; RAVI, S. // Journal of Applied Probability;Jun2014, Vol. 51 Issue 2, p528
As the name suggests, the family of general error distributions has been used to model nonnormal errors in a variety of situations. In this article we show that the asymptotic distribution of linearly normalized partial maxima of random observations from the general error distributions is Gumbel...

- ON ASYMPTOTICALLY LACUNARY STATISTICAL EQUIVALENT SEQUENCES IN PROBALISTIC NORMED SPACE. Esi, Ayhan // Journal of Mathematics & Statistics;2013, Vol. 9 Issue 2, p144
In this study we study the new concept of asymptotically lacunary statistical convergent sequences in probabilistic normed spaces and prove some basic properties.

- A Proof of Walsh's Convergence Theorem Using Couplings. Austin, Tim // IMRN: International Mathematics Research Notices;2015, Vol. 2015 Issue 15, p6661
By using the q-analog of van der Corput's method, we study the divisor function in an arithmetic progression to modulus q. We show that the expected asymptotic formula holds for a larger range of q than was previously known, provided that q has a certain factorization.

- MICROPULSES AND DIFFERENT TYPES OF BROWNIAN MOTION. MAROUBY, MATTHIEU // Journal of Applied Probability;Sep2011, Vol. 48 Issue 3, p792
In this paper we study sums of micropulses that generate different kinds of processes. Fractional Brownian motion and bifractional Brownian motion are obtained as limit processes. Moreover, we not only prove the convergence of finite-dimensional laws but also, in some cases, convergence in...