In the plane, we define a fractal known as the Vicsek snowflake in terms of a family of affine contractions in 2. We show that the Vicsek snowflake is a nested fractal in the sense of Lindstrøm (1990). We define random walks on the Vicsek snowflake and explicitly find an invariant probability...

The noncentral [chi]2 random variable can be written as the sum of two independent random variables one of which is a (central) [chi]2 random variable and the other is known as the [chi]2 random variable with zero d.f. We give a probabilistic proof of this by using properties of the square of a...