Current Developments in Mathematics
Hyperbolicity and stable polynomials in combinatorics and probability
These lectures survey the theory of hyperbolic and stable polynomials, from their origins in the theory of linear PDEs to their present uses in combinatorics and probability theory.
amoeba; cone; dual cone; Gaarding-hyperbolicity; generating function; half-plane property; homogeneous polynomial; Laguerre-Pólya class; multiplier sequence; multi-affine; multivariate stability; negative dependence; negative association; Newton’s inequalities; Rayleigh property; real roots;semi-continuity; stochastic covering; stochastic domination; total positivity
2010 Mathematics Subject Classification
Primary 26C10, 62H20. Secondary 05A15, 30C15.