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On the greedy cleaning problem

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On the greedy cleaning problem

Laurent Tournier (LAGA, Université Paris 13)

Joint work with Vladas Sidoravicius and Leonardo Rolla (IMPA)

Probability seminar, Weizmann Institute July 3, 2013

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on R 2

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on R 2

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on R 2

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on R 2

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on R 2

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on R 2

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on R 2

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on R 2

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

(10)

Greedy cleaner on R 2

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

(11)

Greedy cleaner on R 2

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on R 2

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on R 2

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on R 2

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on R 2

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on R 2

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on R 2

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on R 2

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on R 2

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on R 2

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on R 2

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on the strip [0, 5] × R

-50000 0 50000 100000 150000 200000

0 100000 200000 300000 400000 500000 600000 700000 800000 900000 1e+06 Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on the strip [0, 5] × R

-5000 0 5000 10000 15000 20000

0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on the strip [0, 5] × R

-1000 -800 -600 -400 -200 0 200 400 600 800 1000 1200

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on the strip [0, 5] × R

(1000 steps, stretched width)

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on line with p = 1 of double points

-100000 0 100000 200000 300000 400000 500000 600000 700000 800000 900000 1e+06

0 200000 400000 600000 800000 1e+06 1.2e+06 1.4e+06 1.6e+06 1.8e+06 2e+06

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on line with p = 1 of double points

-10000 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000

0 20000 40000 60000 80000 100000 120000 140000 160000 180000 200000

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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Greedy cleaner on line with p = 1 of double points

-2000 -1000 0 1000 2000 3000 4000 5000 6000 7000 8000 9000

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Laurent Tournier (LAGA, Paris 13) Greedy cleaner

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