分野別セミナー

First-passage percolation is a random growth model which has a metric structure. An Infinite geodesic is an infinite sequence whose all sub-sequences are shortest paths. One of the important objects is the number of infinite geodesics originating from the origin. When the dimension is two and an edge distribution is continuous, it is proved to be almost surely constant [D. Ahlberg, C. Hoffman. Random coalescing geodesics in first-passage percolation]. In this talk, we will discuss the above result for other dimensions and general distributions. In the proof, we use the random coalescing property, which is itself important.