Speaker: Parthanil Roy

Title: Hopf Decomposition of Nonsingular Z^d-Actions and 
Long Range Dependence of Stationary
S\alphaS Random Fields

Abstract: Jan Rosinski (2000) obtained a decomposition of a stationary
symmetric \alpha-stable random field into three independent parts.
This work establishes the connection between this decomposition and
Hopf decomposition of nonsingular Z^d-actions. With the
help of this connection, we study a partial maxima sequence of the
stable random field. Depending on the ergodic theoretical structures
of the underlying group action, we observe different kinds of
asymptotic behavior of this partial maxima sequence and argue that
this may indicate a phase transition from short memory to long
memory. (This is a joint work with Gennady Samorodnitsky.)