Steepest descent

We study unitary random matrix ensembles of the form −1 Zn,N | det M |2α e−N Tr V (M ) dM, where α −1/2 and V is such that the limiting mean eigenvalue density for n, N → ∞ and n/N → 1 vanishes quadratically at the origin. In order to compute the double scaling limits of the eigenvalue correlation kernel near the origin, we use the Deift/Zhou steepest descent method applied to the Riemann-Hilbert problem for orthogonal polynomials on the real line with respect to the weight |x|2α e−N V (x) . ...

42p dontetvui 17-01-2013 73 7   Download

We study several constrained variational problems in the 2-Wasserstein metric for which the set of probability densities satisfying the constraint is not closed. For example, given a probability density F0 on Rd and a time-step 2 h 0, we seek to minimize I(F ) = hS(F )+W2 (F0 , F ) over all of the probability densities F that have the same mean and variance as F0 , where S(F ) is the entropy of F . We prove existence of minimizers. We also analyze the induced geometry of the set of densities satisfying the constraint on...

41p tuanloccuoi 04-01-2013 49 7   Download

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Hybrid Steepest Descent Method with Variable Parameters for General Variational Inequalities Yanrong Yu and Rudong Chen

14p sting10 07-03-2012 42 3   Download

Một bước rất quan trọng của mạng neuron đó là việc huấn luyện mạng (training) hay còn gọi là việc học Huấn luyện x1 W2 Đầu ra...

22p ngochaigl 25-06-2011 160 50   Download