2014/09/24 by Jianping Jiang, Jiang, Jianping · 1 citation
Computer Science · Decision Sciences · Engineering · Mathematics · #60J67 #60K35 #82B43 #Business #Distributed and Parallel Computing Systems #FOS: Mathematics #Probability (math.PR) #Reservoir Engineering and Simulation Methods #Scientific Computing and Data Management #math.PR #msc:60J67 #msc:60K35 #msc:82B43
paper · pdf · doi:10.48550/arxiv.1409.6834
Some corrections. To appear in Markov Processes and Related Fields
openalex publication_date 2014/09/24 · arxiv created 2017/06/04 · arxiv updated 2017/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define radial exploration processes from a to b and from b to a in a domain D of hexagons where a is a boundary point and b is an interior point. We prove the reversibility: the time-reversal of the process from b to a has the same distribution as the process from a to b. We show the scaling limit of such an exploration process is a radial SLE6 in D. As a consequence, the distribution of the last hitting point with the boundary of any radial SLE6 is harmonic measure. We also prove the scaling limit of a similar exploration process defined in the full complex plane ℂ is a full-plane SLE6. A by-product of these results is that the time-reversal of a radial SLE6 trace after the last visit to the boundary is a full-plane SLE6 trace up to the first visit of the boundary.