Prior information and ambiguity, ill-posed problems by Jaynes E.T. PDF

By Jaynes E.T.

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In this case the marginal distributions of the interparticle distances are also identical, but they are clearly not independent, since they are constrained to obey triangle inequalities (for example). The simplest form of the independent pairs approximation consists in assuming that the interparticle distances are also independent, except that when reaction occurs all the distances involving the reacting particles are removed along with the particles. Thus, given that there are N unreacted particles at time t, there are N(N — l)/2 interparticle distances, each of which is equally likely to be the next pair to encounter, and each of which will make a reactive encounter in the interval [t,t + dt} with probability X ( t } d t .

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