Abstract. We examine the convexity of the hitting distribution of the real axis for symmetric random walks on $\duz ^2$. We prove that for a random walk starting at $(0,h)$, the hitting distribution is convex on $[h-2,\infty )\cap\duz $ if $h\ge2$. We also show an analogous fact for higher-dimensional discrete random walks. This paper extends the results of a recent paper [NT].

DOI: 10.14232/actasm-014-526-1

AMS Subject Classification (1991): 60G50; 05A20

Keyword(s): discrete random walk, integer lattice, convexity

Received April 2, 2014. (Registered under 26/2014.)