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We consider the problem of determining the arrival statistics of unbiasedplanar random walkers to complex target configurations. In contrast to problemsposed in finite domains, simple moments of the distribution, such as the mean(MFPT) and variance, are not defined and it is necessary to obtain the fullarrival statistics. We describe several methods to obtain these distributionsand other associated quantities such as splitting probabilities. One approachcombines a Laplace transform of the underlying parabolic equation with matchedasymptotic analysis followed by numerical transform inversion. The secondapproach is similar, but uses a boundary integral equation method to solve forthe Laplace transformed variable. To validate the results of this theory, andto obtain the arrival time statistics in very general configurations ofabsorbers, we introduce an efficient Kinetic Monte Carlo (KMC) method thatdescribes trajectories as a combination of large but exactly solvableprojection steps. The effectiveness of these methodologies is demonstrated on avariety of challenging examples highlighting the applicability of these methodsto a variety of practical scenarios, such as source inference. A particularlyuseful finding arising from these results is that homogenization theories, inwhich complex configurations are replaced by equivalent simple ones, areremarkably effective at describing arrival time statistics.

Trapping of Planar Brownian Motion: Full First Passage Time Distributions by Kinetic Monte-Carlo, Asymptotic and Boundary Integral Methods