Construction of stationary discs for perturbations of decoupled submanifolds in $\mathbb{C}^4$
We construct generalized stationary discs to perturbations of decoupled real submanifolds of codimension $2$ in $\mathbb{C}^4$.
math.CV↗
arXiv subjects
Jad Mchaimech
Publications and source records attributed to Jad Mchaimech.
Zero-one laws for events with positional symmetries
We use an information-theoretic argument due to O'Connell (2000) to prove that every sufficiently symmetric event concerning a countably infinite family of independent and identically distributed random variables is deterministic (i.e., has a probability of either 0 or 1). The i.i.d. condition can be relaxed. This result encompasses the Hewitt-Savage zero-one law and the ergodicity of the Bernoulli process, but also applies to other scenarios such as infinite random graphs and simple renormalization processes.
math.PR↗