Introduction to the Monte Carlo method

The expression "Monte Carlo method" is actually very general. Monte Carlo (MC) methods are stochastic techniques-meaning they are based on the use of random numbers and probability statistics to investigate problems. You can find MC methods used in everything from economics to nuclear physics to regulating the flow of traffic. Of course the way they are applied varies widely from field to field. But, strictly speaking, to call something a "Monte Carlo" experiment, all you need to do is use random numbers to examine some problem. The use of MC methods to model physical problems allows us to examine more complex systems than we otherwise can. Solving equations which describe the interactions between two atoms is fairly simple; solving the same equations for hundreds or thousands of atoms is impossible. With MC methods, a large system can be sampled in a number of random configurations, and that data can be used to describe the system as a whole.

More about Monte Carlo methods:
On course home page: http://phycomp.technion.ac.il/~comphy/classfiles/mci.html
Computational Science Education Project: http://csep1.phy.ornl.gov/mc/mc.html
Daniel Ellard S-Q book: http://www.eecs.harvard.edu/~ellard/Q-97/HTML/root/node36.html

Monte Carlo method for polymer transport problem: sampling rule

The first step: Following the rule of probability calculation we made string of # the neighbor and his probability for example:

The second step: Cumulative function calculation

When probabilities to hop are known and normalized we build cumulative probability function by consecutively cumulating (adding) all probabilities:

The third step

We generate 1 random number uniformly distributed from 0 to 1 (let's take for example 0.67 )  and search which interval in cumulative probability function contains this number.

We see that random chose drop out on neighbor number 4.