9,161 research outputs found
Central limit theorems for random polytopes in a smooth convex set
Let be a smooth convex set with volume one in \BBR^d. Choose random
points in independently according to the uniform distribution. The convex
hull of these points, denoted by , is called a {\it random polytope}. We
prove that several key functionals of satisfy the central limit theorem
as tends to infinity.Comment: 23 pages, no figur
Private manufacturing SMEs survival and growth in Vietnam: The role of export participation
This study investigates for the first time a linkage between export participation and firm performance in terms of survival and profit growth in Vietnam. Using an unbalanced panel dataset from 2005 to 2009, our study shows no difference in the survival probability between exporters and non-exporters. By digging deeper to export status at different stages, the results indicate that continuous exporters have a positive association with probability of survival whereas export stoppers indicate a negative relationship. In terms of the relationship between firm growth and export activity, using Average Treatment Effects (OLS), export status is not related to firm profit growth. However, the Quantile Treatment Effects estimates reveal that export participation is positively and statistically significant associated with firms having profit growth above the median. The above findings might imply that exporting promoting policies, coupled with policies maintaining positions of firms in export market could be helpful since this may help firms improve their survival probability and profit growth
Random matrices: Universal properties of eigenvectors
The four moment theorem asserts, roughly speaking, that the joint
distribution of a small number of eigenvalues of a Wigner random matrix (when
measured at the scale of the mean eigenvalue spacing) depends only on the first
four moments of the entries of the matrix. In this paper, we extend the four
moment theorem to also cover the coefficients of the \emph{eigenvectors} of a
Wigner random matrix. A similar result (with different hypotheses) has been
proved recently by Knowles and Yin, using a different method.
As an application, we prove some central limit theorems for these
eigenvectors. In another application, we prove a universality result for the
resolvent, up to the real axis. This implies universality of the inverse
matrix.Comment: 25 pages, no figures, to appear, Random Matrices: Theory and
applications. This is the final version, incorporating the referee's
suggestion
The spectrum of random kernel matrices: universality results for rough and varying kernels
We consider random matrices whose entries are f() or f(||Xi-Xj||^2)
for iid vectors Xi in R^p with normalized distribution. Assuming that f is
sufficiently smooth and the distribution of Xi's is sufficiently nice, El
Karoui [17] showed that the spectral distributions of these matrices behave as
if f is linear in the Marchenko--Pastur limit. When Xi's are Gaussian vectors,
variants of this phenomenon were recently proved for varying kernels, i.e. when
f may depend on p, by Cheng and Singer [13]. Two results are shown in this
paper: first it is shown that for a large class of distributions the regularity
assumptions on f in El Karoui's results can be reduced to minimal; and secondly
it is shown that the Gaussian assumptions in Cheng--Singer's result can be
removed, answering a question posed in [13] about the universality of the
limiting spectral distribution.Comment: 25 pages, referees' suggestions and corrections incorporated, to
appear in Random Matrices: Theory and Application
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