【摘要】 <正> §1 引言自从Spitzer 1970年提出简单排它过程的概率模型以来,Liggett和Spitzer在七十年代初对它做了大量的工作。在迁移概率对称或平移不变或可逆正常返的条件下,他们基本解决了过程的遍历性。最近Arratia又研究了该过程中带有标记的质点的极限定理。作者在[10]更多还原

【Abstract】 Let S be a countable set. X={0, 1, …, m}^s. P(=（p（x, y））_x,y∈s) a transition probability matrix, g （·） is a strictly monotonically increasing function with g （0） = 0. We say that （{η_t}, P^η） is a generalized simple exclusion process if it is uniquely determined by the generator Ωf（η） =sum from u∈Bg（η（u））sum from v∈S P（u, v） [f(η_uv)—f（η）], f∈（X）, η∈X. where （X） is the set of the all cylindrical functions on X; if η（u） =0 orη（v） =m or u=v then η（uv）=η, otherwise η_uv（u）=η（u）—1, η_uv（v）=η（v） +1, η_uv（w）=η（w）, w{u, v}. When m=1, it is a simple exclusion process proposed and studied by Spitzer and Liggett. When ≥1 and P is positive recurrent and reversible, we obtained the ergodic theorem. In this paper we deal with the case of m≥1 and a potential random walk P. We obtain the description of all the translation invariant and invariant measures for the processes. A part of results of Liggett on simple exclusion processes is extended. Theorem. Let 3=Z^d, P is a potential irreducible random walk on Z^d. Then the set of all extreme points of the translation invariant and invariant measures for the process coincides with {V_p: O≤ρ≤∞}, where V_o and v_∞ are the unit masses on 0（0∈X, 0（x）=0, x∈S） and M（M∈X, M（x）=m, x∈S） respectively; v_o （0<ρ<∞）are product measures with marginal distributions v_o（η（x）=k）=P^k/（g（k）g（k-1）…g（1））/sum from i=1 to m P^t（g（i）g（i-1）…g（1））+1 0≤k≤m, x∈S.更多还原