最后通行渗流中最可能的测地线
On the most likely geodesic in last passage percolation
AI总结：
本研究探讨最后通行渗流中最可能的测地线问题，确定三种利于极端角路径的机制，在指数最后通行渗流中证明角路径近乎典型，并推测测地线概率单调性在一般情况下成立。
AI中文摘要：
我们研究最后通行渗流中识别最可能作为测地线出现的路径的问题。直觉表明，这些典型路径应为极端角路径，即在可达顶点立方体的角之间直线延伸的路径。我们确定了三种有利于此类角路径的机制，并证明它们比除极少量路径外的所有路径都更可能出现。我们在指数最后通行渗流中进行了更具体的比较，其中适度偏差估计可用于证明角路径在精确意义上近乎典型。最后，我们在特殊情况下证明了测地线概率的一种单调性形式，并推测该性质在一般情况下成立。
英文摘要：
We consider the problem of identifying the paths most likely to occur as geodesics in last passage percolation. Heuristics suggest that these modal paths should be the extreme corner paths, going straight between the corners of the cube of accessible vertices. We identify three mechanisms which favour such corner paths, and show that they are more likely to appear than all but a vanishingly small portion of paths. We make more specific comparisons in exponential last passage percolation, where moderate deviation estimates may be used to show that corner paths are nearly modal in a precise sense. Finally, we show a form of monotonicity of geodesic probabilities in a special case and conjecture that this holds in general.
