The Brownian Castle

نویسندگان

چکیده

We introduce a 1+1-dimensional temperature-dependent model such that the classical ballistic deposition is recovered as its zero-temperature limit. Its ∞-temperature version, which we refer to 0-Ballistic Deposition (0-BD) model, randomly evolving interface which, surprisingly enough, does not belong either Edwards–Wilkinson (EW) or Kardar–Parisi–Zhang (KPZ) universality class. show 0-BD has scaling limit, new stochastic process call Brownian Castle (BC) although it “free”, distinct from EW and, like any other renormalisation fixed point, scale-invariant, in this case under 1:1:2 (as opposed 1:2:3 for KPZ and 1:2:4 EW). In present article, only derive finite-dimensional distributions, but also provide “global” construction of advantage highlighting fact admits backward characteristics given by (backward) Web (see [37, 16]). Among others, characterisation enables us establish fine pathwise properties BC relate these special points Web. prove (strong) Markov Feller on suitable space càdlàg functions determine long-time behaviour. Finally, give glimpse proving convergence rather strong sense. © 2022 The Authors. Communications Pure Applied Mathematics published Wiley Periodicals LLC.

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ژورنال

عنوان ژورنال: Communications on Pure and Applied Mathematics

سال: 2022

ISSN: ['1097-0312', '0010-3640']

DOI: https://doi.org/10.1002/cpa.22085