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Description: |
Deterministic dynamics on stationary point process in R^d are built upon compatible point-shifts: translation invariant mappings from each point of the process to another. When a point-shift is applied multiple times to a point-process it creates a sequence of distributions, namely, the distributions of point process given there is a point of the nth iteration of the point-shift at the origin. We introduce the notion of marked stochastic point-shifts. Marked point-shifts use not only the realization of the point-process to decide how to map each point of the process, but also extra information coming from enlarging the probability space through marks. Then we reproduce the dynamics of deterministic point-shifts in the space of marked point processes. However, we show that the two dynamics: on the marked space and on the non-marked space do not, in general, commute. We provide conditions under they do.
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Date: |
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| Start Time: |
14:30 |
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Speaker: |
Antonio Sodre (Department of Mathematics, Univ. of Texas at Austin)
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Institution: |
Department of Mathematics, Univ. of Texas at Austin
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Place: |
Sala 5.5
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| Research Groups: |
-Probability and Statistics
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See more:
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