### random walk

(movement with random turns)

The term **random walk** is used for a kind of motion
(or mathematically-equivalent process) where after some length in
one direction, the direction shifts to an unrelated random direction.
The concept is used to describe/model some processes, including
some in financial investing, some in biology, as well some
in physics, e.g., **statistical physics**.

For example, in radiative transfer, when a photon
is absorbed by an atom, and later one is emitted, the direction
of the new photon is random, having no relation to the direction
of the one earlier received.

Mathematical (statistical) properties of random walks are studied,
one being that the average straight-line distance traveled after N
such random travel legs is the length of "the square root N" legs.
Given the radiative transfer example, this means photons leaving
stars have been absorbed and re-emitted on the order of the square
of the number of legs (average distance a photon travels before
being re-absorbed) that would be necessary if the photon's direction
was always outward. For the Sun, a typical leg in the photon's
journey is on the order of a centimeter and it can take thousands
or even a million years for a photon to leave the Sun after the
creation of the photon (by the heat from fusion in the
stellar core) that began the random walk.

(*mathematics,simulations,computation*)
**Further reading:**

https://en.wikipedia.org/wiki/Random_walk

**Referenced by pages:**

Eddington approximation

radiation zone

spectral energy distribution (SED)

two-stream approximation

Index