Random walk in R

randomwalk.R

library(ggplot2)

walk <- function(N, p = 0.5) {
  cumsum((-1)^rbinom(N, 1, 1 - p))
}

# Convergence of the random walk
l <- sapply(1:1000, function(n){
  N <- 100
  tail(walk(N, 0.5), 1)
})

plot(density(l))
x <- seq(min(l), max(l), len = 100)
hx <- dnorm(x, mean(l), sd(l)) 
lines(x, hx, col = 'red')

# Display 3 random walks
N <- 1000
a <- walk(N, p = 0.5)
b <- walk(N, p = 0.45)
c <- walk(N, p = 0.40)

df <- data.frame(x = rep(1:N, 3), y = c(a, b, c), idx = rep(c('a', 'b', 'c'), each = N))

ggplot(df) + 
  geom_line(aes(x = x, y = y, colour = idx)) +
  scale_color_brewer(palette = 'Dark2') +
  theme_bw()