Ranked functionals of Brownian excursions |
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| Affiliation: | 1. Statistics Department, Evans Hall, University of California at Berkeley, CA 94720, U.S.A.;1. Institute of Mathematical Sciences, Homi Bhaba National Institute (HBNI), IV Cross Road, Taramani, Chennai 600113, India;2. National Institute for Theoretical Physics, School of Physics and Mandelstam Institute for Theoretical Physics, University of the Witwatersrand, Wits, 2050, South Africa;3. Department of Physics, Indian Institute of Science Education and Research Bhopal, Bhopal Bypass, Bhopal 462066, India;4. School of Physics, Indian Institute of Science Education and Research Thiruvananthapuram, Vithura 695551, Kerala, India;1. Department of Radiology, Imperial College Healthcare Trust, St Mary''s Hospital, Praed St, London W2 1NY, UK;2. Department of Radiology, University Hospitals Birmingham, UK;3. Department of Radiology, University Hospitals Manchester, UK;4. North West London Trauma Network, Imperial College Healthcare Trust, St Mary''s Hospital, Praed St, London W2 1NY, UK;5. Department of Surgery, Imperial College Healthcare NHS London, UK;6. National Clinical Director for Trauma, NHS-England, Skipton House, London, UK;1. Department of Mathematics, Massachusetts Institute of Technology, United States;2. NCCR/SwissMAP, Geneva University, Switzerland;3. Yau Mathematical Sciences Center, Tsinghua University, China |
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| Abstract: | It was shown, in our previous work, that the law of the sequence of normalized ranked lengths of Brownian excursions considered up to a random time T is the same for a large class of random times T.We present now some results about (unnormalized) ranked heights of Brownian excursions, which although quite different from those obtained for the lengths, have led us to extend the scope of both studies. |
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