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

[leonne]

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 = N^1/2l

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 N^1/2=$$\tau$$_$$\lambda$$( 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

 

[jack7992]

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.

 

[D H]

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.

 

[jack7992]

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.

 

[leonne]

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