The reunions of three dissimilar vicious walkers
The reunions of three dissimilar vicious walkers
复制标题
三个不同的恶行者的重逢
DOI：
--
复制
发表时间：
1988
期刊：
影响因子：
--
通讯作者：
M. P. Gelfand
中科院分区：
文献类型：
--
作者：
M. Fisher;M. P. Gelfand
本文研究了三个具有任意扩散率b12，b22，b32的一维自由扩散的“恶性”随机游动者的行为，只是它们的路径可能不相交。完整的分布函数在连续极限下精确计算;控制概率衰减的指数为
$$R_n^{（3）} sim 1/n^{psi _3 } $$
所有三个步行者在台阶后的一次不愉快的团聚被发现根据以下条件不断变化：
$$psi _3 = 1 + pi /cos ^{ - 1} left{ {b_2^2 /left[ {（b_1^2 + b_2^2）（b_2^2 + b_3^2）}
{1/2} }
八}$$
.这种变化对（1+1）维中的各种界面润湿转变具有影响。它也可能是相关的直接界面-壁相互作用的边际性衰减为W 0/l2的中间波动制度的（1+1）维润湿，其中指数连续变化与W 0最近被发现。
AbstractWe study the behavior of three “vicious” random walkers which diffuse freely in one dimension witharbitrary diffusivitiesb12,b22,b32, except that their paths may not cross. The full distribution function is calculated exactly in the continuum limit; the exponent ψ3 governing the decay of the probability
$$R_n^{(3)} sim 1/n^{psi _3 } $$
of a simultaneousreunion of all three walkers aftern steps is found to varycontinuously according to
$$psi _3 = 1 + pi /cos ^{ - 1} left{ {b_2^2 /left[ {(b_1^2 + b_2^2 )(b_2^2 + b_3^2 )}
ight]^{1/2} }
ight}$$
. This variation has consequences for various interfacial wetting transitions in (1+1) dimensions. It may also be related heuristically to the marginality of direct interface-wall interactions decaying asW0/l2 in the intermediate fluctuation regime of (1+1)-dimensional wetting, where exponents varying continuously withW0 have recently been found.