
TL;DR
This paper introduces the Brownian Castle, a new scale-invariant stochastic process emerging as the limit of a temperature-dependent ballistic deposition model, distinct from classical universality classes, with detailed construction and properties.
Contribution
It defines the Brownian Castle as a new universality class, providing its finite-dimensional distributions, pathwise properties, and convergence from the 0-Ballistic Deposition model.
Findings
Brownian Castle is a new scale-invariant process.
It is distinct from EW and KPZ universality classes.
The paper establishes convergence from 0-BD to BC.
Abstract
We introduce a -dimensional temperature-dependent model such that the classical ballistic deposition model is recovered as its zero-temperature limit. Its -temperature version, which we refer to as the -Ballistic Deposition (-BD) model, is a randomly evolving interface which, surprisingly enough, does {\it not} belong to either the Edwards--Wilkinson (EW) or the Kardar--Parisi--Zhang (KPZ) universality class. We show that -BD has a scaling limit, a new stochastic process that we call {\it Brownian Castle} (BC) which, although it is "free", is distinct from EW and, like any other renormalisation fixed point, is scale-invariant, in this case under the scaling (as opposed to for KPZ and for EW). In the present article, we not only derive its finite-dimensional distributions, but also provide a "global" construction of the Brownian Castle which…
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