A little bit more about ergodicity Jana Rodriguez Hertz ICTP 2018 - PowerPoint PPT Presentation

counting fish mixing properties ergodicity possibility 3 possibility 3

counting fish mixing properties ergodicity possibility 3 possibility 3 - trace

counting fish mixing properties ergodicity estimate recaptured sample

counting fish mixing properties ergodicity estimate recaptured sample

counting fish mixing properties ergodicity estimate recaptured sample

counting fish mixing properties ergodicity estimate recaptured sample

counting fish mixing properties ergodicity estimate recaptured sample

counting fish mixing properties ergodicity estimate recaptured sample estimated population ? 1000

counting fish mixing properties ergodicity possibility 3 in this example � ∃ lim m ( A ∩ f n ( A )) m ( A )

counting fish mixing properties ergodicity possibility 3 in this example � ∃ lim m ( A ∩ f n ( A )) m ( A ) what about this: N − 1 m ( A ∩ f n ( A )) 1 ? � → N m ( A ) n = 0

counting fish mixing properties ergodicity ergodicity ergodicity (exercise) f : L → L is ergoodic

counting fish mixing properties ergodicity ergodicity ergodicity (exercise) f : L → L is ergoodic if every pair of samples A , B ⊂ L satisfy

counting fish mixing properties ergodicity ergodicity ergodicity (exercise) f : L → L is ergoodic if every pair of samples A , B ⊂ L satisfy N − 1 1 � m ( A ∩ f n ( B )) → m ( A ) m ( B ) N n = 0

counting fish mixing properties ergodicity ergodic property in our context if the lake population is ergodic

counting fish mixing properties ergodicity ergodic property in our context if the lake population is ergodic A ⊂ L initial sample

counting fish mixing properties ergodicity ergodic property in our context if the lake population is ergodic A ⊂ L initial sample N − 1 m ( A ∩ f n ( A )) 1 � N m ( A ) n = 0

counting fish mixing properties ergodicity ergodic property in our context if the lake population is ergodic A ⊂ L initial sample N − 1 m ( A ∩ f n ( A )) 1 � → m ( A ) N m ( A ) n = 0

counting fish mixing properties ergodicity m ( A ∩ f n ( A )) � N − 1 1 → m ( A ) n = 0 m ( A ) N

counting fish mixing properties ergodicity m ( A ∩ f n ( A )) � N − 1 1 → m ( A ) n = 0 m ( A ) N

counting fish mixing properties ergodicity m ( A ∩ f n ( A )) � N − 1 1 → m ( A ) n = 0 m ( A ) N

counting fish mixing properties ergodicity m ( A ∩ f n ( A )) � N − 1 1 → m ( A ) n = 0 m ( A ) N

counting fish mixing properties ergodicity m ( A ∩ f n ( A )) � N − 1 1 → m ( A ) n = 0 m ( A ) N

counting fish mixing properties ergodicity m ( A ∩ f n ( A )) � N − 1 1 → m ( A ) n = 0 m ( A ) N