Branching random walk

<p>In <a href="/facts/Probability_theory/mFBn51rE">probability theory</a>, a branching random walk is a <a href="/facts/Stochastic_process/Ng1n1dnB">stochastic process</a> that generalizes both the concept of a <a href="/facts/Random_walk/08v0jmfv">random walk</a> and of a <a href="/facts/Branching_process/JzdGdWrQ">branching process</a>.  At every generation (a <a href="/facts/Discrete_time/RR8wpS9e">point of discrete time</a>), a branching random walk's value is a set of elements that are located in some <a href="/facts/Linear_space/M1pxMLx2">linear space</a>, such as the <a href="/facts/Real_line/6eq42xX5">real line</a>. Each element of a given generation can have several descendants in the next generation. The location of any descendant is the sum of its parent's location and a <a href="/facts/Random_variable/TwTBXnLT">random variable</a>.
</p><p>This process is a spatial expansion of the <a href="/facts/Galton%E2%80%93Watson_process/9hv6EdPN">Galton–Watson process</a>. Its continuous equivalent is called branching Brownian motion.
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Branching random walk open-in-new

Branching random walk