Aggregation is the key to succeed in random walks

• Two individuals moving according to a discrete random walk with boundaries can increase the probability of winning if they dedicate a fraction θ of their movements to remain aggregated.
• Simulations show that the probability of winning reaches a maximum for the couple as increases, then the probability decreases.
• It seems that this strategy is more efficient the larger the group size, although then the group will move slower.
• This strategy is suggested as a possible underlying mechanism that compels animals to travel in groups.

In a random walk (RW) in ZZ an individual starts at 0 and moves at discrete unitary steps to the right or left with respective probabilities p   and 1−p1−p. Assuming p > 1/2 and finite a, a > 1, the probability that state a   will be reached before −a−a is Q(a, p) where Q(a, p) > p. Here we introduce the cooperative random walk (CRW) involving two individuals that move independently according to a RW each but dedicate a fraction of time θ to approach the other one unit. This simple strategy seems to be effective in increasing the expected number of individuals arriving to a first. We conjecture that this is a possible underlying mechanism for efficient animal migration under noisy conditions.