Consider a system of particles evolving as independent and identically distributed (i.i.d.) random walks. Initial fluctuations in the particle density get translated over time with velocity [(v)vec]vec{v}, the common mean velocity of the random walks. Consider a box centered around an observer who starts at the origin and moves with constant velocity [(v)vec]vec{v}. To observe interesting fluctuations beyond the translation of initial density fluctuations, we measure the net flux of particles over time into this moving box. We call this the “box-current” process.
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