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

Distinct distances on regular varieties over finite fields

In this paper we study some generalized versions of a recent result due to Covert, Koh, and Pi (2015). More precisely, we prove that if a subset $\mathcal{E}$ in a regular variety satisfies $|\mathcal{E}|\gg q^{\frac{d-1}{2}+\frac{1}{k-1}}$, then $\Delta_{k, F}(\mathcal{E})\supseteq \mathbb{F}_q\setminus \{0\}$ for some certain families of polynomials $F(\mathbf{x})\in \mathbb{F}_q[x_1, \ldots, x_d]$

Economic Reform in Tanzania and Vietnam: A Comparative Commentary

The economic reforms in Tanzania and Vietnam represent the two typical cases of transition economies in Asia and Africa, particularrly the transformation of the two developing economies from the planned to the market mechanism. In this paper, the two authors, Brian - a British economist and Dinh - a Vietnamese economist, have, basing on a comparative approach, enquired into various economic and social aspects of the economic reforms in the two countries, including the demographic transition, the change in population growth, the investment in human capital, the growth of GDP, the structural sransformation, the linkage between gricultural growth, rural development, food production and poverty alleviation, the reform in the industrial sector and the state enterprises, the change of ownership , the role of the State, the capital formation, the role of the domestic savings, foreign aid, investment and trade, the gains and losses from globalisation, with an aim to find the answer to the question why in the two cases, Tanzania seemed to follow the donors’ guidance better than Vietnam, but achieved smaller successes?http://deepblue.lib.umich.edu/bitstream/2027.42/40092/3/wp706.pd