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Random walks constitute a fundamental model in probability theory, widely employed to elucidate diffusion processes and random fluctuations in disordered systems. The Gaussian free field (GFF) ...

We study the asymptotic behavior of a multidimensional random walk in a general cone. We find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk ...

Why is it that when you walk randomly, the more you walk, the farther you get from your starting point?