论文标题
用$ p $粘的重尾弹道沉积模型的缩放限制
Scaling limit of the heavy-tailed ballistic deposition model with $p$-sticking
论文作者
论文摘要
弹道沉积是一种经典模型，用于界面增长，其中单位块在$ \ m athbb {z} $的不同站点随机垂直下降，并在接触的第一点上坚持到界面，从而使其生长。我们考虑了该模型的替代版本，其中块具有随机高度为i.i.d。用重（右）的尾巴，每个块在与概率$ p $的第一接触点上粘在界面上（否则，它会直接向下掉落，直到它落在属于接口的块上）。我们研究了$ p $的不同值所得界面的缩放限制，并表明$ p $从$ 1 $ $ 0 $ $ $ 0 $。
Ballistic deposition is a classical model for interface growth in which unit blocks fall down vertically at random on the different sites of $\mathbb{Z}$ and stick to the interface at the first point of contact, causing it to grow. We consider an alternative version of this model in which the blocks have random heights which are i.i.d. with a heavy (right) tail, and where each block sticks to the interface at the first point of contact with probability $p$ (otherwise, it falls straight down until it lands on a block belonging to the interface). We study scaling limits of the resulting interface for the different values of $p$ and show that there is a phase transition as $p$ goes from $1$ to $0$.
