Solution to Random Walk Problem | n_i

In summary, the conversation discusses the concept of a random walk in which a certain number of steps are taken at various lengths and the resulting distance from the starting point is calculated. The root mean square of this distance, σ, can be expressed as a sum of the squared individual step lengths, with probabilities taken into account. However, the exact expression for σ is still unclear.
  • #1
arcTomato
105
27
Homework Statement
Prove that the root mean square deviation for a walk involving the sum of different numbers n of steps of length λ
Relevant Equations
random walk
246472

I don't have any idea to prove this 😢
##n_i##is number of trial, right?
 
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  • #2
arcTomato said:
##n_i##is number of trial, right?
##n_i## is the number of steps in the ith trial
 
  • #3
I got it.
So,I think (4-12)means ##σ=Σ_in_iλ_i^2##, but I don't understand what is this 😢
 
  • #4
arcTomato said:
I got it.
So,I think (4-12)means ##σ=Σ_in_iλ_i^2##, but I don't understand what is this 😢
You need to start from the other end.
You have a random walk in which n1 steps are of length λ1, n2 steps are of length λ2, and so on. I presume you are to take these as all being in the same straight line.
At the end of this walk you are at distance X from where you started. Can you write an expression for σ, the root mean square of X?
 
  • #5
haruspex said:
Can you write an expression for σ, the root mean square of X?
uhh, I don't know how.
##σ^2=<X^2>=<(n_1λ_1+n_2λ_2+,,,,,n_iλ_i)^2>=<(n_1λ_1)^2>+<(n_2λ_2)^2>+,,,,,,##
like this??
 
  • #6
arcTomato said:
uhh, I don't know how.
##σ^2=<X^2>=<(n_1λ_1+n_2λ_2+,,,,,n_iλ_i)^2>=<(n_1λ_1)^2>+<(n_2λ_2)^2>+,,,,,,##
like this??
No, you need some probabilities in there. Each step can be either way.
 
  • #7
probabilities??like this??
246487
 

FAQ: Solution to Random Walk Problem | n_i

What is the "Random Walk Problem"?

The Random Walk Problem is a mathematical concept that describes the movement of a particle or object in a random or unpredictable manner. It is a simple model that has numerous applications in various fields, including physics, biology, economics, and computer science.

How is the "n_i" value used in the Solution to Random Walk Problem?

The "n_i" value in the Solution to Random Walk Problem is the number of steps taken by the particle or object in a particular direction. It is used to calculate the probability of the particle reaching a specific location or state after a given number of steps.

What is the significance of the Solution to Random Walk Problem in science?

The Solution to Random Walk Problem has significant implications in science as it provides a fundamental understanding of the behavior of random processes and systems. It is used to model and analyze a wide range of phenomena, including diffusion, chemical reactions, and stock market fluctuations.

How can the Solution to Random Walk Problem be applied in real-life situations?

The Solution to Random Walk Problem can be applied in various real-life situations, such as predicting the spread of diseases, tracking the movement of molecules in a cell, and analyzing financial data. It can also be used to optimize transportation routes and simulate the movement of animals in their natural habitats.

Are there any limitations to the Solution to Random Walk Problem?

Like any mathematical model, the Solution to Random Walk Problem has its limitations. It assumes that the movement of the particle or object is completely random, which may not always be the case in real-life situations. Additionally, it does not account for external factors that may affect the movement of the particle, such as obstacles or forces.

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