Spectrum of non-Hermitian heavy tailed random matrices

Let (X_{jk})_{j,k>=1} be i.i.d. complex random variables such that |X_{jk}| is in the domain of attraction of an alpha-stable law, with 0< alpha <2. Our main result is a heavy tailed counterpart of Girko's circular law. Namely, under some additional smoothness assumptions on the law of X_{jk}, we prove that there exists a deterministic sequence a_n ~ n^{1/alpha} and a probability measure mu_alpha on C depending only on alpha such that with probability one, the empirical distribution of the eigenvalues of the rescaled matrix a_n^{-1} (X_{jk})_{1<=j,k<=n} converges weakly to mu_alpha as n tends to infinity. Our approach combines Aldous & Steele's objective method with Girko's Hermitization using logarithmic potentials. The underlying limiting object is defined on a bipartized version of Aldous' Poisson Weighted Infinite Tree. Recursive relations on the tree provide some properties of mu_alpha. In contrast with the Hermitian case, we find that mu_alpha is not heavy tailed.Comment: Expanded version of a paper published in Communications in Mathematical Physics 307, 513-560 (2011

Circular Law Theorem for Random Markov Matrices

Consider an nxn random matrix X with i.i.d. nonnegative entries with bounded density, mean m, and finite positive variance sigma^2. Let M be the nxn random Markov matrix with i.i.d. rows obtained from X by dividing each row of X by its sum. In particular, when X11 follows an exponential law, then M belongs to the Dirichlet Markov Ensemble of random stochastic matrices. Our main result states that with probability one, the counting probability measure of the complex spectrum of n^(1/2)M converges weakly as n tends to infinity to the uniform law on the centered disk of radius sigma/m. The bounded density assumption is purely technical and comes from the way we control the operator norm of the resolvent.Comment: technical update via http://HAL.archives-ouvertes.f

TO BLOW THE WHISTLE OR NOT: THE ROLES OF PERCEIVED ORGANIZATIONAL RETALIATION AND UPWARD COMMUNICATION SATISFACTION IN EMPLOYEE RESPONSES TO OBSERVED WRONGDOING

The act of reporting illegal and unethical practices in the workplace has become an increasingly important issue for researchers and organizational management over the past several decades. This study tested a model of whistle-blowing in which perceived organizational retaliation and upward communication satisfaction were hypothesized to act as predictors of types of whistleblowing intentions using a representative sample of employees working in Kirklareli, Turkey (n = 1,012). Structural equation modeling indicated that perceptions of upward communication satisfaction were positively associated to blowing the whistle to internal channels like immediate supervisor and upper management and negatively related to staying silent and external whistleblowing. In addition, perceived threat of retaliation from an organization was negatively related to blowing the whistle to internal channels and positively related to staying silent and external whistleblowing. The present study has contributed to our understanding of whistleblowing in a relatively new national context by clarifying its associations with perceived organizational retaliation and communication with management.WOS:0005626219000122-s2.0-8506548440