Reinforced Random Walk

نویسندگان

  • Henrik Renlund
  • Sven Erick Alm
چکیده

This thesis aim is to present results on a stochastic model called reinforced random walk. This process was conceived in the late 1980’s by Coppersmith and Diaconis and can be regarded as a generalization of a random walk on a weighted graph. These reinforced walks have non-homogeneous transition probabilities, which arise from an interaction between the process and the weights. We survey articles on the subject, perform simulations and extend a theorem by Pemantle.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An expansion for self-interacting random walks

We derive a perturbation expansion for general interacting random walks, where steps are made on the basis of the history of the path. Examples of models where this expansion applies are reinforced random walk, excited random walk, the true (weakly) self-avoiding walk and loop-erased random walk. We use the expansion to prove a law of large numbers and central limit theorem for two models: (i) ...

متن کامل

How edge reinforced random walk arises naturally

We give a characterization of a modi ed edge reinforced random walk in terms of certain partially exchangeable sequences In particu lar we obtain a characterization of edge reinforced random walk in troduced by Coppersmith and Diaconis on a edge connected graph Modifying the notion of partial exchangeability introduced by Diaco nis and Freedman in we characterize unique mixtures of reversible M...

متن کامل

Excited Random Walk in Three Dimensions Has Positive Speed

Excited random walk is a model of a random walk on Z which, whenever it encounters a new vertex it receives a push toward a specific direction, call it the “right”, while when it reaches a vertex it “already knows”, it performs a simple random walk. This model has been suggested in [BW] and had since got lots of attention, see [V, Z]. The reason for the interest is that it is situated very natu...

متن کامل

On Some Generalized Reinforced Random Walk on Integers

We consider Reinforced Random Walks where transition probabilities are a function of the proportion of times the walk has traversed an edge. We give conditions for recurrence or transience. A phase transition is observed, similar to Pemantle [Pem1] on trees.

متن کامل

Directionally Reinforced Random Walks

This paper introduces and analyzes a class of directionally reinforced random walks The work is motivated by an elementary model for time and space correlations in ocean surface wave elds We develop some basic properties of these walks For instance we investigate recurrence properties and give conditions under which the limiting continuous versions of the walks are Gaussian di usion processes M...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005