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Using a novel theoretical approach, we study the mean first-encounter time (MFET) between the two ends of a polymer. Previous approaches used various simplifications that reduced the complexity of the problem, leading, however, to incompatible results. We construct here for the first time a general theory that allows us to compute the MFET. The method is… (More)
In  an example presented a Hausdorff continuous, u.s.c. and l.s.c. multifunction from 〈−1, 0〉 to R which had no continuous selection. The multifunction was not locally Lipschitz. In this paper we show that a locally Lipschitz multifunction from R to a Banach space, which has ”locally finitely dimensional“ closed values does have a continuous selection.
We study the probability of two Brownian particles to meet before one of them exits a finite interval. We obtain an explicit expression for the probability as a function of the initial distance of the two particles using the Weierstrass elliptic function. We also find the law of the meeting location. Brownian simulations show the accuracy of our analysis.… (More)