Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Dr. Yi Shen, University of Waterloo, Canada
Inviter:
王勇 副研究员
Title:
Operator-scaling Gaussian random fields via aggregation
Time & Venue:
2018.8.31 16:00 N620
Abstract:
We propose an aggregated random-field model, and investigate the scaling limits of the aggregated partial-sum random fields. In this model, each copy in the aggregation is a +1/-1 valued random field built from two correlated one-dimensional random walks, the law of each determined by a random persistence parameter. A flexible joint distribution of the two parameters is introduced, and given the parameters the two correlated random walks are conditionally independent. For the aggregated random field for which the persistence parameters are dependent, we show that the scaling limit depends on the growth rates of the underlying rectangular region along two directions: at different rates different operator-scaling Gaussian random fields appear as the region area tends to infinity. In particular, at the so-called critical speed, a large family of Gaussian random fields with long-range dependence arise in the limit. We also identify four different regimes at non-critical speed where fractional Brownian sheets arise in the limit. This is a joint work with Yizao Wang.