Open Science Projects
This page is dedicated to projects and ideas which I more or less pursued at some point but do not find the time to continue. The most recent state of the project is presented in each post. If one is currently work in progress, it is mentioned at the top of the post and in the excerpt as well. I invite you to continue with them as you see fit. I only ask you to contact me when you pick up on one of them, using the given ID, so that I can make a note on the corresponding post that it is work in progress. If someone else wants to join in, I will contact you, asking for news and whether the other person might join in. The idea derives obviously from the polymaths project but on a smaller scale.
We lift the analysis of the Deffuant model with \(k\) agents exhibiting opinions absolutely continuous with respect to Lebesgue measure to the manifold of the densities implied by the model. We conjecture that there is an embedding into 3-dim. space based on the two model parameters and a fixed initial density for i.i.d. opinions with a unique singularity. This singularity gives the limit law of the model and is probably given by a Dirac delta over the projection of the support of the \(k\) product of the initial density to the digonal of the \(k\) cube.
We consider the positive cone of the $d$-dimensional grid and apply to any vertex a logarithm, where the basis is at first irrelevant. We observe in the $2$-dimensional case that along the diagonal the cab driver distance of grid points converges to $0$ but the distance between points of the form $(a,x)$ and $(x,x)$ grow infinitely far appart as $x$ goes to infinity. The project is designed to investigate the implied geometry of the log grid.
