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The leaky Abelian sandpile model (Leaky-ASM) is a growth model in which   $n$   grains of sand start at the origin in   $\mathbb{Z}^2$   and diffuse along the vertices according to a toppling rule. A site can topple if its amount of sand is above a threshold. In each topple, a site sends some sand to each neighbor and leaks a portion   $1-1/d$   of its sand. We compute the limit shape as a function of   $d$   in the symmetric case where each topple sends an equal amount of sand to each neighbor. The limit shape converges to a circle as   $d\to 1$   and a diamond as   $d\to \infty $  . We compute the limit shape by comparing the odometer function at a site to the probability that a killed random walk dies at that site. When   $d\to 1$  , the Leaky-ASM converges to the ASM with a modified initial configuration. We also prove that the limit shape is a circle when simultaneously with   $n\to \infty $   we have that   $d=d_n$   converges to   $1$   slower than any power of   $n$  . To gain information about the ASM, faster convergence is necessary.

The Limit Shape of the Leaky Abelian Sandpile Model