We illustrate a metric geometry viewpoint for large deviation principles by analyzing the proof of a long-standing conjecture on an explicit Schilder-type theorem for super-Brownian motions given by the authors recent...We illustrate a metric geometry viewpoint for large deviation principles by analyzing the proof of a long-standing conjecture on an explicit Schilder-type theorem for super-Brownian motions given by the authors recently,and by understanding sample path large deviations for Fleming-Viot processes.展开更多
The strong embeddability is a notion of metric geometry, which is an intermediate property lying between coarse embeddability and property A. In this paper, we study the permanence properties of strong embeddability f...The strong embeddability is a notion of metric geometry, which is an intermediate property lying between coarse embeddability and property A. In this paper, we study the permanence properties of strong embeddability for metric spaces. We show that strong embeddability is coarsely invariant and it is closed under taking subspaces, direct products, direct limits and finite unions. Furthermore, we show that a metric space is strongly embeddable if and only if it has weak finite decomposition complexity with respect to strong embeddability.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.10971106 and 11271204)
文摘We illustrate a metric geometry viewpoint for large deviation principles by analyzing the proof of a long-standing conjecture on an explicit Schilder-type theorem for super-Brownian motions given by the authors recently,and by understanding sample path large deviations for Fleming-Viot processes.
基金Supported by National Natural Science Foundation of China(Grant No.11231002)
文摘The strong embeddability is a notion of metric geometry, which is an intermediate property lying between coarse embeddability and property A. In this paper, we study the permanence properties of strong embeddability for metric spaces. We show that strong embeddability is coarsely invariant and it is closed under taking subspaces, direct products, direct limits and finite unions. Furthermore, we show that a metric space is strongly embeddable if and only if it has weak finite decomposition complexity with respect to strong embeddability.
