How Do You Calculate the Number of Steps in a Random Walk?

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Homework Help Overview

The discussion revolves around calculating the number of steps in a random walk, specifically addressing the relationship between the total distance traveled and the number of steps taken. The original poster expresses confusion regarding the equations related to the random walk and the implications of step length and time.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to understand how to determine the number of steps (N) in relation to the total distance (L) and step length (l). Some participants question the validity of the original equation provided by the poster, suggesting an alternative formulation. Others introduce concepts of randomness and displacement versus total distance, prompting further clarification on definitions.

Discussion Status

The discussion is active, with participants exploring different interpretations of the problem. Some guidance has been offered regarding the equations, and there is an acknowledgment of the need to clarify definitions related to distance and displacement in the context of a random walk.

Contextual Notes

Participants are navigating potential misunderstandings about the equations and the nature of random walks. There is mention of specific terms and symbols that may require further explanation, as well as the original poster's reference to time and its relationship to step length.

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Question about "random walk"

Homework Statement

.
.. Recall that in a random walk where each step
has length l, the total distance traveled after N steps is L = N1/2l

Homework Equations


The Attempt at a Solution


My problem is the N number of steps, not sure how i would find that.
I saw in the book saying N1/2=\tau\lambda( its subscript lambda idk why always looks so weird)
I thought its the same as \tau which i found a formula l/v
but when i plug into the formula to find L i get (cm)(s) as units, which i don't think its right.
edit
ok reading my notes, it said soothing about, each step takes time \tau I found the time its the l/v , but not sure what to do next
any help thanks
 
Last edited:
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first, is your initial equation right. L= N^(1/2) * l ? That doesn't make sense. I think that should be L = N * l, i.e. if you take 3 steps of 5 units each step, the total distance traveled is 15 units.
 


jack7992 said:
first, is your initial equation right. L= N^(1/2) * l ? That doesn't make sense. I think that should be L = N * l, i.e. if you take 3 steps of 5 units each step, the total distance traveled is 15 units.
You and the original poster are forgetting about randomness here. At each time the step might be step forward, but it might also be backward. If the walk starts at the origin the mean will always be zero. The standard deviation won't be zero. This grows as the square root of N, the number of steps.
 


right, but I was thinking more along the lines of total distance traveled, as in if you walk a mile one way and then come back on the same path, the total distance traveled is two miles, but the total displacement, if you will, is 0. I thought the former is what he was asking about. But I guess it depends on what your trying to define.
 


yeah thxs for the help i figured it out. We where told the L~R so we just solve for N. I thought we had to find L. then plug N into this other formula to find the time. And the original formal i had is right
 

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