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The Small-Community Phenomenon in Networks     The Small-Community Phenomenon  Probability  Networks       font style='font-size:12px;'> 2011/9/22
Abstract: We investigate several geometric models of network which simultaneously have some nice global properties, that the small diameter property, the small-community phenomenon, which is defined t...
Abstract: Consider the stochastic differential equation in $\rr^d$ dX^{\e}_t&=b(X^{\e}_t)dt+\sqrt{\e}\sigma(X^\e_t)dB_t X^{\e}_0&=x_0,\quad x_0\in\rr^d where $b:\rr^d\rightarrow\rr^d$ is $C^1$ s...
Abstract: The uniqueness argument in the proof of Theorem 5, p. 483, of "Small noise asymptotics for invariant densities for a class of diffusions: a control theoretic view, J. Math. Anal. and Appl. (...
We specify a small set, consisting of O(d(log log d)2) points,that intersects the basins under Newton's method of all roots of all (suitably normalized) complex polynomials of xed degrees d, with arb...

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