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Example of the Random Path (Rando Walk)
Storyboard

The random path is a typical example as starting from microscopic probabilities (the step to the right or left) it is possible to develop a probability distribution that accounts for the most probable places in which the walker can be found.

>Model

ID:(308, 0)


Random walk problem
Image

The problem of the random path is an example of how one can from the microscopic description predict the probable temporal evolution. In this case it is assumed that an actor (particle, person, etc.) randomly chooses whether to take a step to the right or to the left. It is assumed that the steps have a length a and that the probability of going to the right is p and to the left q:

ID:(11396, 0)


Binomial distribution
Image

The result of the calculation corresponds to what is called a binomial distribution. Each line indicates the fraction of times that after a number N of steps the actor ends up in that position. This corresponds to the probability of finding it after N steps at that location:

ID:(11397, 0)


Example of the Random Path (Rando Walk)
Model

The random path is a typical example as starting from microscopic probabilities (the step to the right or left) it is possible to develop a probability distribution that accounts for the most probable places in which the walker can be found.

Variables
Symbol
Text
Variable
Value
Units
Calculate
MKS Value
MKS Units
$C_{n_1n_2}$
C_n1n2
Combinaciones posibles de (n_1,n_2) caminos
-
$n_2$
n_2
Número de pasos hacia la derecha
-
$q$
q
Número de pasos hacia la derecha
-
$n_1$
n_1
Número de pasos hacia la izquierda
-
$N$
N
Número total de pasos
-
$n$
n
Número totales de pasos a la izquierda
-
$s$
s
Posición camino aleatorio
m
$P_N(m)$
P_Nm
Probabilidad de $n_1$ de $N$ pasos hacia la izquierda
-
$p_{n_1n_2}$
p_n1n2
Probabilidad de avanzar una combinación (n_1,n_2)
-
$p$
p
Probabilidad de pasos hacia la izquierda
-
$p_{n_1,n_2}$
p_n1n2
Probabilidad de realizar (n_1,n_2) pasos
-
$W_N(n_1,n_2)$
W_n1n2
Probabilidad de realizar (n_1,n_2) pasos cualquier secuencia
-
$a$
a
Step size
m
$\Delta t$
Dt
Tiempo del paso
s
$t$
t
Tiempo final
s

Calculations

First, select the equation:   to ,  then, select the variable:   to 
Symbol
Equation
Solved
Translated

Calculations

Symbol
Equation
Solved
Translated

 Variable   Given   Calculate   Target :   Equation   To be used


Equations

Examples

The problem of the random path is an example of how one can from the microscopic description predict the probable temporal evolution. In this case it is assumed that an actor (particle, person, etc.) randomly chooses whether to take a step to the right or to the left. It is assumed that the steps have a length a and that the probability of going to the right is p and to the left q:

(ID 11396)

The result of the calculation corresponds to what is called a binomial distribution. Each line indicates the fraction of times that after a number N of steps the actor ends up in that position. This corresponds to the probability of finding it after N steps at that location:

(ID 11397)

ID:(308, 0)