Negative dependence and the geometry of polynomials
Babbage, Pembroke St.
We present a powerful tool in the emerging theory of negative dependence. The knowledge of the zeros of the generating (partition) function of your discrete probability measure can be of help when it comes to proving negative dependence properties, just as it is in the Lee-Yang program on phase transitions.
The connection with the geometry of zeros of (multivariate) polynomials allows one to use strong results due to Grace-Walsh-Szegö and Gårding. A consequence is that the symmetric exclusion process with product initial distribution is negatively associated at positive times, as conjectured by Liggett and Pemantle. We also generalize recent work of Lyons on determinantal measures.
This is based on joint work with J. Borcea (Stockholm) and T. M. Liggett (UCLA)
- http://www.math.kth.se/~pbranden/ - Links to relevant papers/preprints