Zeros of a two-parameter random walk∗
نویسندگان
چکیده
We prove that the number γN of the zeros of a two-parameter simple random walk in its first N × N time steps is almost surely equal to N as N →∞. This is in contrast with our earlier joint effort with Z. Shi [4]; that work shows that the number of zero crossings in the first N × N time steps is N (3/2)+o(1) as N → ∞. We prove also that the number of zeros on the diagonal in the first N time steps is ((2π)−1/2 + o(1)) logN almost surely.
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