Finance Math, Discrete Tomography, and the Zeros of Random Polynomials

Larry Shepp (AT \& T Bell Laboratories, Inc.)

Where are the zeros of a polynomial of degree n with real iid standard normal coeffs? Can one reconstruct a finite subset S of the integer lattice Z^2 given the number of points of S on any line in any one of k fixed directions? - a "real" problem. Suppose a company has to choose between corporate options, each returning a profit stream which is a Brownian motion process with known drift and volatility; which option to choose? If Sn is the sum of iid normals with 0 mean and unit variance, then E|Sn| == sqrt(2n/pi); is there any other law besides the standard normal that can make that statement?