Chains with local correlations asymptotically Brownian

4 Chains with local correlations asymptotically Brownian) 

There is a whole class of chains for which the interactions between links involve only neighbours of finite order not larger than p. Thus, for a chain with nearest link interaction (p = 1), we have (N - number of links) 

When the interaction between links extends to neighbours of order p, formula (3.4.54) takes a more general form and we may set 

Of course, the last term results from boundary effects this does not mean, however, that there is any dissymmetry between the extremities of the chain (see above the case where p = 1). 

Of course, the weight associated with a configuration is (see Chapter 2, Section 2.1) 

---