Instituto Nacional de Matemática Pura e Aplicada

Delayed Logistic Equation as a Limit of Long Memory Markov Chains

Abstract We introduce and analyze a long memory continuous-time Markov chain on $${\mathbb R}_+$$ R + whose jump mechanism depends explicitly on a state in the past. From the present state $$x_0$$ x 0 , the process jumps to $$x_0(1+\frac{1}{N})$$ x 0 ( 1 + 1 N ) or to $$x_0(1-\fr...

Linear Fluctuation of Interfaces in Glauber–Kawasaki Dynamics

Abstract In this article, we find a scaling limit of the space-time mass fluctuation field of Glauber + Kawasaki particle dynamics around its hydrodynamic mean curvature interface limit. Here, the Glauber rates are scaled by $$K=K_N$$ K = K N (with $$K_N\uparrow \infty $$ K N ↑ ∞...

A Polynomial Improvement for the Odd Cycle–Complete Ramsey Numbers

Abstract We give a polynomial improvement to the cycle-complete Ramsey numbers $$\begin{aligned} r(C_{\ell },K_k) \geqslant k^{1+\frac{1}{\ell -2} + \varepsilon _{\ell } + o(1)}, \end{aligned}$$ r ( C ℓ , K k ) ⩾ k 1 + 1 ℓ - 2 + ε ℓ + o ( 1 ) , for all fixed odd $$\ell > 7$$ ℓ >...

A Generalization of Marstrand’s Theorem and Some Geometric Applications

Abstract In this paper we prove using quite elementary methods, with a combinatorial nature, two general results related to Marstrand’s projection theorem in a quite general formulation over metric spaces under a suitable transversality condition (the “projections" are in princip...

Existence of minimal surfaces in infinite-volume hyperbolic 3-manifolds

Abstract The existence of embedded minimal surfaces in non-compact 3-manifolds remains a largely unresolved and challenging problem in geometry. In this paper, we address several open cases regarding the existence of finite-area, embedded, complete, minimal surfaces in infinite-v...