Hydrodynamic Limit of the Symmetric Exclusion Process on a Compact Riemannian Manifold

We consider the symmetric exclusion process on suitable random grids that approximate a compact Riemannian manifold. We prove that a class of random walks on these random grids converge to Brownian motion on the manifold. We then consider the empirical density field of the symmetric exclusion process and prove that it converges to the solution of the heat equation on the manifold.

A New Visual Multi-Secrets Sharing Scheme by Random Grids

In (2, 2)-visual secret sharing (VSS) schemes, a common type of (k, n)-threshold VSS schemes, secret information can be decoded directly through only two shares by using a human vision system. Several studies have analyzed methods of simplifying the decoding process and refining encoding to pass more secret images through two identical shares. However, limited secret images are retrieved, and the quality of the recovered images is low. This paper proposes an advanced (2, 2)-VSS scheme that can embed N secret images into two rectangular shares. Compared with other related VSS schemes, more secret images can be encrypted and the distortion is adjustable in the proposed scheme, yielding more flexibility in theory and practice.