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Consider a general random walk on ℤ together with an i.i.d. random coloring of ℤ. The -process is the one where time is indexed by ℤ, and at each unit of time we see the step taken by the walk together with the color of the newly arrived at location. S. Kalikow proved that if = 1 and the random walk is simple, then this process is not Bernoulli. We generalize his result by proving that it is not Bernoulli in, Bernoulli but not Weak Bernoulli in = 3 and 4, and Weak Bernoulli in 5. These properties are related to the intersection behavior of the past and the future of simple random walk. We obtain similar results for general random walks on ℤ, leading to an almost complete classification. For example, in = 1, if a step of size has probability proportional to l/|x|  0), then the -process is not Bernoulli when α ≥2, Bernoulli but not Weak Bernoulli when 3/2 ≤α < 2, and Weak Bernoulli when 1 < α < 3/2.

Mixing properties of the generalized T, T-1-process