Recall that the Ising model (see other posts) is a well-known model in statistical physics, which describes magnetization phenomena. Our previous explorations of the Ising model where based on the Glauber interpretation of the Ising model, but this interpretation is not the only interpretation. While most of the other interpretations are qualitatively similar to the Glauber interpretation (e.g., Metropolis interpretation), this time we will present you interpretation, which is very much different from the Glauber interpretation - Kawasaki interpretation.

In this rather dated video (back from 2011) prof. Rob Axtell (one of the contemporary gurus of agent-based modeling and general interdisciplinary numerical simulation) talks about the possibilities of agent-based models. He also talks about his work in modeling of the economy with huge number of agents.

Controversial debates are often marked by an emergence of polarized state. In this post we will consider yet another variation of the voter model proposed by a group of German researchers [1], which shows that significant repulsion leads to the polarized fifty-fifty state.

It might sound strange, but statistics and geometry are very much related. Result in one is likely to have some meaning in the other. This time Numberphile has teamed up with another my favorite 3Blue1Brown to explore a game using darts.

As it is assumed that a random (unskilled) player plays the game, his plays simply explore a continuous phase space. Each point in the said phase space corresponding to all possible events in the game. To keep playing the game the player has to satisfy a condition, which provides us a boundary in the phase spaces. Conveniently geometric shape enclosed by the boundary is a ball (or a hyper-sphere). So our problem of calculating probability is reduced to a problem of figuring out the ball's volume in respect to the size of phase space. More details in the video below.

Last time we have proposed the agent-based cobweb model. In certain case price time series of this model exhibit different volatility. So this time we will take a look at price change statistics in this model. As is common for our financial markets posts we will consider probability density functions and spectral density.