Non-local energetics of random heterogeneous lattices

An equivalence functor between local vector lattices and vector lattices

We call a local vector lattice any vector lattice with a distinguished positive strong unit and having exactly one maximal ideal (its radical). We provide a short study of local vector lattices. In this regards, some characterizations of local vector lattices are given. For instance, we prove that a vector lattice with a distinguished strong unit is local if and only if it is clean with non no-...

A Local Limit Theorem for Random Walks in Random Scenery and on Randomly Oriented Lattices

Random walks in random scenery are processes defined by Zn := ∑n k=1 ξX1+...+Xk , where (Xk, k ≥ 1) and (ξy, y ∈ Z) are two independent sequences of i.i.d. random variables. We assume here that their distributions belong to the normal domain of attraction of stable laws with index α ∈ (0, 2] and β ∈ (0, 2] respectively. These processes were first studied by H. Kesten and F. Spitzer, who proved ...

Random Dispersal vs Non-Local Dispersal

Random dispersal is essentially a local behavior which describes the movement of organisms between adjacent spatial locations. However, the movements and interactions of some organisms can occur between non-adjacent spatial locations. To address the question about which dispersal strategy can convey some competitive advantage, we consider a mathematical model consisting of one reaction-diffusio...

Random access codes and non-local resources

It is known that a PR-BOX (PR), a non-local resource and (2 → 1) random access code (RAC), a functionality (wherein Alice encodes 2 bits into 1 bit message and Bob learns one of randomly chosen Alice’s inputs) are equivalent under the no-signaling condition. In this work we introduce generalizations to PR and (2→ 1) RAC and study their inter-convertibility. We introduce generalizations based on...

Expected Number of Local Maxima of Some Gaussian Random Polnomials