In this world,

randomness and chance go together in different ways. Random situations can

happen anytime such as when one coincidentally meets somebody they haven’t seen

or met in a while. There could be many factors on how two people or even

objects could randomly meet. This study will provide different factors of how

the coincidental meet up happens using simulations together with the concept of

random walk in probability.

A coincidental meet

up is one of many ways to show a random walk. A random walk is a study in

probability concerning objects rambling from their starting points, this means

that the direction of their step is unplanned. This is when the beauty of a

random walk comes because it is when probability gets involved. Since the

movements are unplanned, it is determined through a probabilistic approach. A

random walk is used in different ways such as biological movement, movement of

atoms and molecules, search engines like Google and even in finance.

The best

representation of how a random walk works is by using the one-dimensional

integer line, having zero as the starting point. Suppose there is a fair coin

with two sides, heads and tails. If it lands heads, move one step to the

positive side or to the right, if it lands tails then move one step to the

negative side or to the left. There could be many things that can be asked from

this, like where will it be after n steps and how many times it would go back

to zero.

The simulation will

involve assuming there are two persons related to each other in some ways and

have not met for a long time, they will be called agents. Although it can also

be interpreted that the two agents are just hardly related to each other.

Suppose they are in the same closed area and far from each other, the time for

them to meet is unknown. The randomness of their movement is set into rules of

either all directions are equally probable, or a certain direction has a higher

probability because of an agent’s certain destination point. There will be

instances where one agent will have a known path which means predicting this

agent’s path is certain. The certainty of this agent’s path is based on how

used it is to its path, a good example is if someone only goes to the grocery

store in a mall to buy some necessities and doesn’t bother to go to other

places in the mall. The decision of the direction of their steps will be by

drawing with choices based on a compass N as north, S as south, W as west, E as

east, NE as north east, NW as north west, SE as south east and SW as south west,

and the rules set for the probability of how they move applicable.