We consider the continuous time symmetric random walk with a slow bond on ℤ, which rates are equal to 1/2 for all bonds, except for the bond of vertices {−1, 0}, which associated rate is given by αn−β ...

First observed by botanist Robert Brown in 1827, Brownian Motion describes the continuous, chaotic movement of tiny particles, such as pollen grains, suspended in a medium. This motion results from ...

The random walk theorem, first presented by French mathematician Louis Bachelier in 1900 and then expanded upon by economist Burton Malkiel in his 1973 book A Random Walk Down Wall Street, asserts ...