论文标题
Bernoulli Gibbsian Line合奏的紧密度
Tightness of Bernoulli Gibbsian line ensembles
论文作者
论文摘要
Bernoulli Gibbsian Line集合$ \ Mathfrak {l} =（l_1，\ dots，l_n）$是$ n-1 $ n opedial bernoulli随机步行者$ l_1，\ dots \ dots，l_ {n-1} $的轨迹的定律$ l_1 \ geq \ cdots \ geq l_n $）。在本文中，我们研究了Bernoulli Gibbsian Line合奏的渐近行为$ \ Mathfrak {l}^n =（l^n_1，\ dots，l^n_n）$当Walkers $ n $的数量趋向于Infinity。我们证明，如果一个人对最低索引（或顶部）曲线的单点边缘$ l_1^n $具有轻度但均匀的控制权，则在线集合的空间中，序列$ \ mathfrak {l}^n $都很紧。此外，我们表明，如果顶部曲线$ l_1^n $以有限维度收敛到抛物线的通风$ _2 $进程，则$ \ mathfrak {l}^n $收敛到抛物面转移的通风线集合。
A Bernoulli Gibbsian line ensemble $\mathfrak{L} = (L_1, \dots, L_N)$ is the law of the trajectories of $N-1$ independent Bernoulli random walkers $L_1, \dots, L_{N-1}$ with possibly random initial and terminal locations that are conditioned to never cross each other or a given random up-right path $L_N$ (i.e. $L_1 \geq \cdots \geq L_N$). In this paper we investigate the asymptotic behavior of sequences of Bernoulli Gibbsian line ensembles $\mathfrak{L}^N = (L^N_1, \dots, L^N_N)$ when the number of walkers $N$ tends to infinity. We prove that if one has mild but uniform control of the one-point marginals of the lowest-indexed (or top) curves $L_1^N$ then the sequence $\mathfrak{L}^N$ is tight in the space of line ensembles. Furthermore, we show that if the top curves $L_1^N$ converge in the finite dimensional sense to the parabolic Airy$_2$ process then $\mathfrak{L}^N$ converge to the parabolically shifted Airy line ensemble.
