论文标题
布朗城堡
The Brownian Castle
论文作者
论文摘要
我们引入了$ 1+1 $维度依赖温度的模型，以使经典的弹道沉积模型被恢复为其零温度极限。它的$ \ infty $ - 温度版本，我们称为$ 0 $ - BALLICICIC SEDISION（$ 0 $ -BD）型号，是一个随机发展的界面，令人惊讶地{\ it not}属于Edwards-willkinson（ew）或Kardar-y-parisi-parisi-parisi-Zhang（kpz kpz kpz kpz）classiale classiale classiale。 We show that $0$-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 $1:1:2$ scaling (as opposed to $1:2:3$ for KPZ and $1:2:4$ for EW).在本文中，我们不仅得出了其有限维分布，而且还提供了布朗城堡的“全球”构建，该构建的优势是强调了一个事实，即它承认了（向后）布朗尼网络给予的向后特征（请参阅[TóthB。 Ann。除其他外，这种表征使我们能够建立卑诗省的良好路径属性，并将其与网络的特殊点联系起来。我们证明，布朗城堡是Càdlàg功能合适空间上的（强）马尔可夫和砍伐过程，并确定其长期行为。最后，我们通过证明$ 0 $ -BD与BC的融合在相当强的意义上瞥见了它的普遍性。
We introduce a $1+1$-dimensional temperature-dependent model such that the classical ballistic deposition model is recovered as its zero-temperature limit. Its $\infty$-temperature version, which we refer to as the $0$-Ballistic Deposition ($0$-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 $0$-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 $1:1:2$ scaling (as opposed to $1:2:3$ for KPZ and $1:2:4$ 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 has the advantage of highlighting the fact that it admits backward characteristics given by the (backward) Brownian Web (see [Tóth B., Werner W., Probab. Theory Related Fields, '98] and [L. R. G. Fontes, M. Isopi, C. M. Newman, and K. Ravishankar, Ann. Probab., '04]). Among others, this characterisation enables us to establish fine pathwise properties of BC and to relate these to special points of the Web. We prove that the Brownian Castle is a (strong) Markov and Feller process on a suitable space of càdlàg functions and determine its long-time behaviour. At last, we give a glimpse to its universality by proving the convergence of $0$-BD to BC in a rather strong sense.
