论文标题
分支随机步行的紧密度在时间内均匀的随机环境
Tightness for branching random walk in time-inhomogeneous random environment
论文作者
论文摘要
我们考虑在时间征收的随机环境中进行分支随机步行，其中$ k $的所有粒子分支到相同的随机数粒子$ \ MATHCAL {l} _ {k+1} \ ge 2 $中，其中$ \ nathcal {l Mathcal {l} _k $，$ k $，$ k \ in \ in \ mathbbbb nardard and and and and and and and and I.i。令$ \ mathbb {p} $表示$（\ Mathcal {l} _K）_ {k \ in \ mathbb {n}} $的定律，然后$ m_n $表示最大粒子在$ n $中的最大粒子的位置。我们证明有$ m_n $，仅函数$（\ nathcal {l} _k）_ {k \ in \ {0，\ dots，n \}} $，因此（相对于$ \ m athbb {p} $）概率。
We consider a branching random walk in time-inhomogeneous random environment, in which all particles at generation $k$ branch into the same random number of particles $\mathcal{L}_{k+1}\ge 2$, where the $\mathcal{L}_k$, $k\in\mathbb{N}$, are i.i.d., and the increments are standard normal. Let $\mathbb{P}$ denote the law of $(\mathcal{L}_k)_{k\in\mathbb{N}}$, and let $M_n$ denote the position of the maximal particle in generation $n$. We prove that there are $m_n$, which are functions of only $(\mathcal{L}_k)_{k\in\{0,\dots, n\}}$, such that (with regard to $\mathbb{P}$) the sequence $(M_n-m_n)_{n\in\mathbb{N}}$ is tight with high probability.
