basic_tools:random_walk
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basic_tools:random_walk [2017/11/10 17:02] jakobadmin [Layman] |
basic_tools:random_walk [2020/04/02 18:12] (current) 74.98.242.130 [Abstract] |
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| ====== Random Walks ====== | ====== Random Walks ====== | ||
| - | <tabbox Why is it interesting?> | + | <tabbox Intuitive> |
| - | + | ||
| - | Random walks are essential to understand Brownian motion, to model stock movements in finance and to understand the [[advanced_tools:path_integral|path integral]] of quantum theories. | + | |
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| - | <tabbox Layman> | + | |
| - | <blockquote>Imagine a man coming out of a bar in cancun, an open bottle of sunscreen dribbling from his back pocket. He walks forward for a few steps, and then there’s a good chance that he will stumble in one direction or another. He steadies himself, takes another step, and then stumbles once again. the direction in which the man stumbles is basically random, at least insofar as it has nothing to do with his purported destination. If the man stumbles o en enough, the path traced by the sunscreen dripping on the ground as he weaves his way back to his hotel (or just as likely in another direction entirely) will look like the path of a dust particle oating in the sunlight. [...] | + | <blockquote>Imagine a man coming out of a bar in cancun, an open bottle of sunscreen dribbling from his back pocket. He walks forward for a few steps, and then there’s a good chance that he will stumble in one direction or another. He steadies himself, takes another step, and then stumbles once again. the direction in which the man stumbles is basically random, at least insofar as it has nothing to do with his purported destination. If the man stumbles o en enough, the path traced by the sunscreen dripping on the ground as he weaves his way back to his hotel (or just as likely in another direction entirely) will look like the path of a dust particle oating in the sunlight. [...] |
| Imagine that the drunkard from cancun is now back at his hotel. He gets out of the elevator and is faced with a long hallway, stretching to both isle and his right. At one end of the hallway is room 700; at the other end is room 799. He is somewhere in the middle, but he has no idea which way to go to get to his room. He stumbles to and fro, half the time moving one way down the hall, and half the time moving in the opposite direction. Here’s the question that the mathematical theory of random walks allows you to answer: Suppose that with each step the drunkard takes, there is a 50% chance that that step will take him a little further toward room 700, at one end of the long hallway, and a 50% chance that it will take him a little further toward room 799, at the other end. What is the probability that, a er one hundred steps, say, or a thousand steps, he is standing in front of a given room? | Imagine that the drunkard from cancun is now back at his hotel. He gets out of the elevator and is faced with a long hallway, stretching to both isle and his right. At one end of the hallway is room 700; at the other end is room 799. He is somewhere in the middle, but he has no idea which way to go to get to his room. He stumbles to and fro, half the time moving one way down the hall, and half the time moving in the opposite direction. Here’s the question that the mathematical theory of random walks allows you to answer: Suppose that with each step the drunkard takes, there is a 50% chance that that step will take him a little further toward room 700, at one end of the long hallway, and a 50% chance that it will take him a little further toward room 799, at the other end. What is the probability that, a er one hundred steps, say, or a thousand steps, he is standing in front of a given room? | ||
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| <cite>The Physics of Wall Street by Weatherall</cite> | <cite>The Physics of Wall Street by Weatherall</cite> | ||
| </blockquote> | </blockquote> | ||
| - | <tabbox Student> | ||
| - | For a nice description see chapter 23 and 24 in Sleeping Beauties in Theoretical Physics by Thanu Padmanabhan | + | <tabbox Concrete> |
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| + | * For a nice description see chapter 23 and 24 in Sleeping Beauties in Theoretical Physics by Thanu Padmanabhan | ||
| + | * and also [[http://pages.physics.cornell.edu/~sethna/StatMech/EntropyOrderParametersComplexity.pdf|Statistical Mechanics: Entropy, Order Parameters, and Complexity]] by Sethna | ||
| + | * B. Hughes (1995), "Random Walks and Random Environments" | ||
| + | * Elements of the Random Walk by Rudnick | ||
| - | <tabbox Researcher> | + | <tabbox Abstract> |
| + | Imagine a man coming out of a bar in cancun, an open bottle of sunscreen dribbling from his back pocket. He walks forward for a few steps, and then there’s a good chance that he will stumble in one direction or another. | ||
| + | |||
| + | Now put that guy on a big canvas with an X and Y dimension. The line his sunscreen drippings will make is a random walk. | ||
| + | |||
| + | The math behind that chaotic process is pretty useful in all kinds of domains, option trading being one in particular. | ||
| + | |||
| + | "How do we model this stock" | ||
| + | |||
| + | "Imagine it's running around like a drunk guy in Cancun" | ||
| + | |||
| + | "Cool" | ||
| <note tip> | <note tip> | ||
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| - | <tabbox Examples> | + | <tabbox Why is it interesting?> |
| - | --> Example1# | + | Random walks are essential to understand Brownian motion, to model stock movements in finance and to understand the [[theories:quantum_mechanics:path_integral|path integral]] of quantum theories. |
| - | |||
| - | <-- | ||
| - | --> Example2:# | + | <tabbox FAQ> |
| - | |||
| - | <-- | ||
| - | <tabbox FAQ> | ||
| --> Why do stocks follow random walks?# | --> Why do stocks follow random walks?# | ||
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| <-- | <-- | ||
| <tabbox History> | <tabbox History> | ||
| + | * An entertaining description can be found in "On the wonderful world of random walks" by E.W. Montroll and M.F. Shlesinger. | ||
| </tabbox> | </tabbox> | ||
basic_tools/random_walk.1510329724.txt.gz · Last modified: 2017/12/04 08:01 (external edit)
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