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What is random walk? Will anyone explain it to me?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

Assuming you mean a random walk on a graph, it means that you first assign probabilities to each node of the graph in question that describe how probable it is to get from one node to another node of the graph and then start at some node of the graph in question and do a random walk with probabilities defined as stated. Wikipedia should really give you a good idea of what random walks are.

They are connected to Markov chain, which are very useful for certain types of probability questions.

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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And what are Random Walk Algorithms?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

http://en.m.wikipedia.org/wiki/Markov_chain_Monte_Carlo#section_1

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

Hi Agnishom;

The most well known of the random walks is the gambler's ruin problem.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

**Online**

It is being said that if a person takes n steps of length 1 each,

then he will be displaced by sqrt(n)**BUT WHY**

It could also be possible that there wasn't any displacement at all

*Last edited by Agnishom (2012-06-27 00:26:13)*

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

Hi Agnishom

I think that is only an estimate. The largest probability for theending point hasthe point which is sqrt(n) away fromthe starting point.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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