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Statistics Seminar. "The ‘coin-turning walk’ and its scaling limit", Janos Englander. Department of Mathematics, University of Colorado Boulder

Seminarium

Tid: 2019-05-17 13:15 till: 14:00
Plats: MH:227
Kontakt: dragi [at] maths [dot] lth [dot] se
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Let S denote the random walk obtained from `coin turning' with some sequence {p_n}_{n\ge 1}, as introduced in [EV2018]. In this paper we investigate the scaling limits of S in the spirit of the classical Donsker invariance principle, for the heating as well as for the cooling dynamics.

In the critical cooling regime, an interesting new process emerges: it is a continuous, piecewise linear, recurrent process, for which the one-dimensional marginals are Beta-distributed.

For the heating dynamics we prove an invariance principle with a non-classical scaling.

We also investigate the recurrence of the walk and its scaling limit, as well as the limiting distribution of the nth step of the walk.