Solving Random Walk Question in 2D Plane | Monte

In summary, the conversation discusses a subproblem of a research project involving a bounded 2d plane and n probes performing random walks. The world is closed, meaning that probes going outside the border reappear on the opposite side. The question posed is how long it will take for all n probes to pass through a stationary circle of radius R. It is suggested that simulations can be used to find the probability of all probes passing through the circle.
  • #1
Monte_Carlo
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Hello Everyone,

The following is a subproblem of research project I'm working on, i.e. not a homework. Let's suppose you have a bounded 2d plane and n distinct probes that do random-walk in that plane. The world is closed in a sense that a probe going outside the border ends up being on the opposite side, e.g. a probe going too far east winds up showing up from the west.

Let's suppose you have a stationary circle of radius R in the plane. How long will it take before each of n probes pass through the circle at least once?

Thanks,

Monte
 
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  • #2
If you can find the probability that a single probe passed through the circle after N steps you can construct the probability that all of them did. I would be surprised if there was an analytic solution, but simulations should work.
 

1. What is a random walk in a 2D plane?

A random walk in a 2D plane is a mathematical concept that describes the movement of a point or particle in a two-dimensional space. It involves taking random steps in any direction and recording the position of the point after each step.

2. What is the purpose of solving a random walk question in a 2D plane?

The purpose of solving a random walk question in a 2D plane is to understand the behavior and patterns of random movements in a two-dimensional space. It has applications in various fields such as physics, biology, and finance.

3. What is the Monte Carlo method in relation to random walks?

The Monte Carlo method is a computational technique used to solve problems by simulating random processes. In the case of a random walk in a 2D plane, the Monte Carlo method can be used to generate random steps and simulate the movement of the point.

4. How is the probability of a random walk in a 2D plane calculated?

The probability of a random walk in a 2D plane can be calculated by considering the number of steps taken, the step size, and the direction of each step. It is also affected by other factors such as boundary conditions and external forces.

5. What are some real-world applications of solving random walk questions in a 2D plane?

Random walks in a 2D plane have many real-world applications. For example, it can be used to model the movement of particles in a liquid or gas, the spread of diseases in a population, and the fluctuations of stock prices in financial markets.

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