Abstract



Almost all of this chapter is a review of the subject advertised in the title, although a few proofs or results are new. There are some references to applications at the end, but the point of view is the one of mathematical physics. The subject of persistent random walks is to broad to be given a fair review of a length appropriate to a chapter, so we have focused on the essentials, which is more or less what is understood by ?random flight?. Although both names refer to the same topic, as explained in this chapter, it has been studied by many physicists under the name ?persistent random walk?, and they naturally tend to find applications and extend their field of study. On the other hand mathematicians have studied the topic under the name ?random flight?, and they have stayed closer to the original problem. The subject of study of this chapter is clearly stated in its first paragraph. Then the first few sections build up progressively to it, while discussing physical models to have a concrete as possible picture of the subject. The main part of the chapter shows the methods that have been applied to solve the problem and the results obtained. The most characteristic feature of this chapter is the central position occupied by the Born expansion, which is an expansion for the solution to our problem indexed by the number of collisions. All the results that have been obtained by other methods can be obtained using the Born expansion, which also gives a physical picture. The last three sections are extensions of the problem stated in the first paragraph of the chapter. The first of these sections, ?Anisotropic scattering?, is useful to firmly bridge what is understood by ?random flight? and by ?persistent random walk?. The choice of the second of these sections, ?Projections onto lower dimensional spaces? is due both to the taste of the author and to the very recent developments. The last section mentions all else that should have been included in a review on the persistent random walk.  
International

Si 


Book Edition


Book Publishing


ISBN

9781614709879 
Series


Book title

Statistical Mechanics and Random Walks: Principles, Processes and Applications 
From page

581 
To page

612 