public 01:34:41

Ben Gaines : TBA

  -   Graduate/Faculty Seminar ( 170 Views )


public 01:34:52

Math Slam! : TBA

  -   Graduate/Faculty Seminar ( 123 Views )

public 01:34:46
public 01:34:51

Math Slam : Math Slam

  -   Graduate/Faculty Seminar ( 124 Views )

Math Slam

public 01:34:03

Jer-Chin (Luke) Chuang : TBA

  -   Graduate/Faculty Seminar ( 145 Views )

public 01:14:59

Dong Yao : Two problems in probability theory

  -   Graduate/Faculty Seminar ( 197 Views )

This talk will be concerned with two problems. The first is the zeros of the derivatives of. Kac random polynomials K_n, which is a random polynomial with i.i.d. coefficients. It has been shown that the empirical measure of zeros of K_n will converge to the uniform measure on the unit circle of complex plane. Same convergence holds true for nay fixed order of derivative of K_n. In a joint work with Renjie Feng, we show if we consider the N_n-th order of derivative of K_n, then asymptotic behavior of empirical measure of this derivative will depend on the limit of \frac{N_n}{n}. In particular, as long as this ratio is greater than 0, the phenomenon of ‘zeros clustering around unit circle’ breaks down. The second talk is about Average Nearest Neighbor Degree (ANND), which is a measure for the degree-degree correlation for complex network. We shall be concerned with the probabilistic properties of ANND in the configuration model. We prove if the variable X generating the network has order of moment larger than 2, then the ANND(k) will converge uniformly to μ2/μ1, where μ2 is the second moment of X, and μ1 is the first moment. For the case that X has infinite variance, we show the pointwise (i.e., for fixed k) scaled convergence of ANND(k) to a stable random variable. This is joint work with Nelly Litvak and Pim van der Hoorn. More recently, Clara Stegehuis showed that when X is sample from the Pareto distribution, then one can obtain a complete spectrum of ANND(k) for the erased configuration model.