central limit theorem for linear eigenvalue statistics of random matrices with independent entries we consider n x n real symmetric and hermitian wigner random matrices n 1 2 w with independent modulo symmetry condition entries and the null sample covariance matrices n 1 x x with independent entries of m x n matrix x assuming first that the 4th cumulant excess 4 of entries of w and x is zero and that their 4th moments satisfy a lindeberg type condition we prove that linear statistics of eigenvalues of the above matrices satisfy the central limit theorem clt as n m m n c 0 oo with the same variance as for gaussian matrices if the test functions of statistics are smooth enough essentially of the class c 5 this is done by using a simple interpolation trick from the known results for the gaussian matrices and the integration by parts presented in the form of certain differentiation formulas then by using a more elaborated version of the techniques we prove the clt in the case of nonzero excess of entries again for essentially 5 test function here the variance of statistics contains an additional term proportional to 4 the proofs of all limit theorems follow essentially the same scheme

on the second mixed moment of the characteristic polynomials of 1d band matrices we consider the asymptotic behavior of the second mixed moment of the characteristic polynomials of 1d gaussian band matrices i e of the hermitian n n matrices h n with independent gaussian entries such that h ij h lk ik jl j ij where j w 2 triangle 1 1 assuming that w 2 n 1 theta 0 theta leq 1 we show that the moment s asymptotic behavior as n to infty in the bulk of the spectrum coincides with that for the gaussian unitary ensemble

testing for structural change in dynamic models the well known cusum test for structural change is investigated whe n there are lagged dependent variables among the regressors in a linear model the authors show that both a modified cusum test suggested b y j m dufour 1982 and the straightforward cusum test retain their asymptotic significance levels in dynamic models and find that the power depends crucially on the angle between the mean regressor and the structural shift copyright 1988 by the econometric society

clt for linear spectral statistics of large dimensional sample covariance matrices let bn 1 n t1 2nxnx nt1 2n where xn xij is n n with i i d complex standardized entries having finite fourth moment and t1 2n is a hermitian square root of the nonnegative definite hermitian matrix tn the limiting behavior as n with n n approaching a positive constant of functionals of the eigenvalues of bn where each is given equal weight is studied due to the limiting behavior of the empirical spectral distribution of bn it is known that these linear spectral statistics converges a s to a nonrandom quantity this paper shows their rate of convergence to be 1 n by proving after proper scaling that they form a tight sequence moreover if exppx211 0 and expp x11 4 2 or if x11 and tn are real and exppx411 3 they are shown to have gaussian limits

hypersingular bem for dynamic fracture in 2 d piezoelectric solids fracture behavior of piezoelectric solids under time harmonic loading is numerically analyzed in this paper a 2 d boundary element method bem based on both displacement and traction boundary integral equations is presented the time harmonic green s functions for the infinite plane are split into singular plus regular terms the singular ones coinciding with the static green s functions in this manner the singular and hypersingular integrals arising in the formulation may be treated by the same simple regularization procedure proposed by the authors for static piezoelectricity quarter point elements are used for the direct evaluation of stress and electric displacement intensity factors from nodal values several numerical examples for the scattering of waves by different crack configurations including branched and curved cracks and crack interaction problems are given to demonstrate the performance of the proposed method 2006 elsevier b v all rights reserved

a new test for structural stability in the linear regression model abstract we propose a new test for the constancy of regression coefficients in linear models the test does not require that possible change points be known we derive the limiting null distribution of the test statistic prove that the test has non trivial power against many local alternatives and show that it compares favourably to both the cusum and cusum of squares tests

a trend resistant test for structural change based on ols residuals abstract we discuss the null distribution and local power of an ols based version of the cusum test and show that this contrary to other tests for structural change like e g the ploberger kontrus kramer fluctuation test can also be applied to trending data

asymptotic theory of a test for the constancy of regression coefficients against the random walk alternative one component of the coefficients follows a random walk process we discuss the limiting null behavior of the test statistic without assuming normality under two situations where the initial value of the random walk process is known or unknown the limiting distribution is that of a quadratic functional of brownian motion and the characteristic function is obtained from the fredhohm determinant associated with a certain integral equation the limiting distribution is then computed by numerical inversion of the characteristic function

central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs diluted regime we study the linear eigenvalue statistics of large random graphs in the regimes when the mean number of edges for each vertex tends to infinity we prove that for a rather wide class of test functions the fluctuations of linear eigenvalue statistics converges in distribution to a gaussian random variable with zero mean and variance which coincides with non gaussian part of the wigner ensemble variance

fluctuations of eigenvalues of patterned random matrices in this article we study the fluctuations of linear statistics of eigenvalues of circulant symmetric circulant reverse circulant and hankel matrices we show that the linear spectral statistics of these matrices converge to the gaussian distribution in total variation norm when the matrices are constructed using independent copies of a standard normal random variable we also calculate the limiting variance of the linear spectral statistics for circulant symmetric circulant and reverse circulant matrices in this article we study the fluctuations of linear statistics of eigenvalues of circulant symmetric circulant reverse circulant and hankel matrices we show that the linear spectral statistics of these matrices converge to the gaussian distribution in total variation norm when the matrices are constructed using independent copies of a standard normal random variable we also calculate the limiting variance of the linear spectral statistics for circulant symmetric circulant and reverse circulant matrices

on fluctuations of eigenvalues of random band matrices we consider the fluctuations of linear eigenvalue statistics of random band n times n matrices whose entries have the form mathcal m ij b 1 2 u 1 2 i j b tilde w ij with i i d tilde w ij possessing the 4 varepsilon th moment where the function u has a finite support c c so that m has only 2c b 1 nonzero diagonals the parameter b called the bandwidth is assumed to grow with n in a way such that b n rightarrow 0 without any additional assumptions on the growth of b we prove clt for linear eigenvalue statistics for a rather wide class of test functions thus we improve and generalize the results of the previous papers jana et al arxiv 1412 2445 li et al random matrices 2 04 2013 where clt was proven under the assumption n b n 1 2 moreover we develop a method which allows to prove automatically the clt for linear eigenvalue statistics of the smooth test functions for almost all classical models of random matrix theory deformed wigner and sample covariance matrices sparse matrices diluted random matrices matrices with heavy tales etc

universality for general wigner type matrices we consider the local eigenvalue distribution of large self adjoint n times n random matrices mathbf h mathbf h with centered independent entries in contrast to previous works the matrix of variances s i j mathbbm e h i j 2 is not assumed to be stochastic hence the density of states is not the wigner semicircle law its possible shapes are described in the companion paper ajanki et al in quadratic vector equations on the complex upper half plane arxiv 1506 05095 we show that as n grows the resolvent mathbf g z mathbf h z 1 converges to a diagonal matrix mathrm diag mathbf m z where mathbf m z m 1 z dots m n z solves the vector equation 1 m i z z sum j s i j m j z that has been analyzed in ajanki et al quadratic vector equations on the complex upper half plane arxiv 1506 05095 we prove a local law down to the smallest spectral resolution scale and bulk universality for both real symmetric and complex hermitian symmetry classes

the cusum test with ols residuals we show that the cusum test of the stability over time of the coefficients of a linear regression model which is usually based on recursive residuals can also be applied to ordinary least squares residuals we derive the limiting null distribution of the resulting test and compare its local power to that of the standard procedure it turns out that neither version is uniformly superior to the other henceforth bde on the cusum and cusum of squares tests for the constancy over time of the coefficients of a linear regression model both tests are based on recursive residuals which are independent n o o 2 under ho and therefore ideal ingredients for all types of tests while the cusum of squares test has been generalized to ordinary least squares ols residuals mccabe and harrison 1980 a generalization of the cusum test to ols residuals which are dependent and heteroskedastic even under ho has not yet been made except for a very special case macneill 1978 in fact both bde 1975 p 151 and mccabe and harrison 1980 p 142 argue that a least squares variant of the cusum test poses intractable problems due to an alleged difficulty in assessing the significance of the departure of the cumulated ols residuals from their mean value zero below we show that it is no more difficult to derive the limiting distribution for a cusum test based on ols residuals than for a cusum test based on recursive residuals while the cusums of the recursive residuals properly standardized tend in distribution to a standard wiener process sen 1982 krimer ploberger and alt 1988 henceforth kpa we show that the ols based cusums tend in distribution to a brownian bridge or tied down brownian motion see billingsley 1968 p 64 this generalizes macneill s 1978 polynomial regression result to arbitrary regressor sequences we also demonstrate that the resulting cusum test has higher local power for certain types of structural change than the one based on recursive residuals though neither variant is uniformly superior to the other

a nonparametric test for changing trends many tests of parameter change in dynamic models exhibit nonmonotonic power an important source of the nonmonotonic power comes from the bias in estimating parameters when there is a change in the deterministic component to avoid this bias we propose a nonparametric test for changing trends based on nonparametrically detrended data the tests are similar in spirit to nonparametric conditional moment tests such as fan and li j nonparametr stat 10 1999a 245 11 1999b 251 and zheng j econometrics 75 1996 263 the resulting statistics have a standard normal distribution a monte carlo experiment suggests that the tests have good power against changes in the deterministic component

central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs we consider the adjacency matrix a of a large random graph and study fluctuations of the function fn z u 1 n k 1nexp ugkk z with g z z ia 1 we prove that the moments of fluctuations normalized by n 1 2 in the limit n satisfy the wick relations for the gaussian random variables this allows us to prove central limit theorem for tr g z and then extend the result on the linear eigenvalue statistics tr a of any function r r which increases together with its first two derivatives at infinity not faster than an exponential

time harmonic green s functions for anisotropic magnetoelectroelasticity abstract two dimensional 2 d and three dimensional 3 d time harmonic green s functions for linear magnetoelectroelastic solids are derived in this paper by means of radon transform displacement field and electric and magnetic potentials in a fully anisotropic magnetoelectroelastic infinite solid due to a time harmonic point force point charge and magnetic monopole are obtained in form of line integrals over a unit circle in 2 d case and surface integrals over a unit sphere in 3 d case this dynamic fundamental solution is then split into the sum of regular dynamic plus singular terms the singular terms coincide with the green s functions for the static problem and may be further reduced to closed form expressions the proposed green s functions can be used in the corresponding boundary element method bem formulation

the dual boundary element method effective implementation for crack problems summary the present paper is concerned with the effective numerical implementation of the two dimensional dual boundary element method for linear elastic crack problems the dual equations of the method are the displacement and the traction boundary integral equations when the displacement equation is applied on one of the crack surfaces and the traction equation on the other general mixed mode crack problems can be solved with a single region formulation both crack surfaces are discretized with discontinuous quadratic boundary elements this strategy not only automatically satisfies the necessary conditions for the existence of the finite part integrals which occur naturally but also circumvents the problem of collocation at crack tips crack kinks and crack edge corners examples of geometries with edge and embedded crack are analysed with the present method highly accurate results are obtained when the stress intensity factor is evaluated with the j integral technique the accuracy and efficiency of the implementation described herein make this formulation ideal for the study of crack growth problems under mixed mode conditions

an energy based criterion of crack branching and its application on the multidimensional space method abstract in this paper a criterion of crack branching based on the energy release rate is proposed theory of multidimensional space method for crack branching is established in the framework of the extended finite element method xfem in which the formula of the boundary shift energy is deduced the boundary cracking energy is obtained because the boundary shift model is abstracted into the boundary cracking model the energy release rates of the crack branching in four quadrants are determined based on boundary cracking energy further the energy release rate of the crack branching is introduced into multidimensional space method to determine the crack branching if the crack tip branching the criteria of crack branching are applied to determine the direction of the branching cracks otherwise the criteria of maximum circumferential stress are applied to determine the direction of the cracks moreover a classical numerical example is investigated to verify the correctness of the criterion of crack branching in the framework of the multidimensional space method

hypersingular integrals in boundary element fracture analysis a new general purpose boundary element method for domains with cracks has been recently developed this technique avoids the use of a multi domain decomposition by including an additional integral equation expressing the boundary condition on the crack the principal requirement of this technique is the analytic determination of certain hypersingular integrals of the green s function which arise from this equation in order to establish the applicability of this method for fracture these integrals are evaluated herein for the kelvin solution of the three dimensional navier equations of linear elasticity numerical results for fracture problems using the single domain boundary element analysis are also presented

analysis of cracked magnetoelectroelastic composites under time harmonic loading this paper presents a numerical model for the analysis of cracked magnetoelectroelastic materials subjected to in plane mechanical electric and magnetic dynamic time harmonic loading a traction boundary integral equation formulation is applied to solve the problem in combination with recently obtained time harmonic green s functions rojas diaz et al 2008 the hypersingular boundary integral equations appearing in the formulation are first regularized via a simple change of variables that permits to isolate the singularities relevant fracture parameters namely stress intensity factors electric displacement intensity factor and magnetic induction intensity factor are directly evaluated as functions of the computed nodal opening displacements and the electric and magnetic potentials jumps across the crack faces the method is checked by comparing numerical results against existing solutions for piezoelectric solids finally numerical results for scattering of plane waves in a magnetoelectroelastic material by different crack configurations are presented for the first time the obtained results are analyzed to evaluate the dependence of the fracture parameters on the coupled magnetoelectromechanical load the crack geometry and the characteristics of the incident wave motion

testing for structural change in conditional models in the past decade we have seen the development of a new set of tests for structural change of unknown timing in regression models most notably the supf statistic of andrews 1993 econometrica 61 825 856 the expf and avef statistics of andrewsploberger 1994 econometrica 62 1383 1414 and the statistic of nyblom 1989 journal of american statistical association 84 223 230 the distribution theory used for these tests is primarily asymptotic and has been derived under the maintained assumption that the regressors are stationary this excludes structural change in the marginal distribution of the regressors as a result these tests technically cannot discriminate between structural change in the conditional and marginal distributions this paper attempts to remedy this de ciency by deriving the large sample distributions of the test statistics allowing for structural change in the marginal distribution of the regressors we nd that the asymptotic distributions of the supf expf avef and statistics are not invariant to structural change in the regressors to solve the size problem we introduce a xed regressor bootstrap which achieves the rst order asymptotic distribution and appears to possess reasonable size properties in small samples our bootstrap theory allows for arbitrary structural change in the regressors including structural shifts polynomial trends and exogenous stochastic trends it allows for lagged dependent variables and heteroskedastic error processes 2000 elsevier science s a all rights reserved

central limit theorems for linear statistics of heavy tailed random matrices we show central limit theorems clt for the stieltjes transforms or more general analytic functions of symmetric matrices with independent heavy tailed entries including entries in the domain of attraction of alpha stable laws and entries with moments exploding with the dimension as in the adjacency matrices of erdos renyi graphs for the second model we also prove a central limit theorem of the moments of its empirical eigenvalues distribution the limit laws are gaussian but unlike to the case of standard wigner matrices the normalization is the one of the classical clt for independent random variables

on asymptotic expansions and scales of spectral universality in band random matrix ensembles we consider real random symmetric n n matrices h of the band type form with characteristic length b the matrix entries are independent gaussian random variables and have the variance proportional to where u t vanishes at infinity we study the resolvent in the limit and obtain the explicit expression for the leading term of the first correlation function of the normalized trace