Long-Time Average of Field Measured by an Ornstein-Uhlenbeck Wanderer(General)

概要

論文の詳細を見る
For a given field V(x) on R^d, we shall find (i) the exponent ν such that X_T[ω]=T^<-v>∫^T_oV(ω(t))dt converges as T→∞ to have a non-trivial probability distribution, and (ii) the distribution itself, where ω(t) denotes the d-dimensional Ornstein-Uhlenbeck process starting from ω(0)=x at t=0. The exponent and the probability distribution are different depending on whether or not a weighted average ∫_<R^d> V(x)exp[-βx^2/2D]d^dx of V vanishes, where D and β are constants of the Ornstein-Uhlenbeck process. In the non-vanishing case, they are ν=1 and a Dirac delta distribution, while in the vanishing case, ν=1/2 and the Gaussian distribution. The results have applications to the physics of chemoreception in immune systems.
社団法人日本物理学会の論文
2006-09-15