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On the cardinality of Hausdorff spaces and Pol-Šapirovskii technique

Alejandro Ramírez-Páramo — 2005

Commentationes Mathematicae Universitatis Carolinae

In this paper we make use of the Pol-Šapirovskii technique to prove three cardinal inequalities. The first two results are due to Fedeli [2] and the third theorem of this paper is a common generalization to: (a) (Arhangel’skii [1]) If X is a T 1 space such that (i) L ( X ) t ( X ) κ , (ii) ψ ( X ) 2 κ , and (iii) for all A [ X ] 2 κ , A ¯ 2 κ , then | X | 2 κ ; and (b) (Fedeli [2]) If X is a T 2 -space then | X | 2 aql ( X ) t ( X ) ψ c ( X ) .

Asymptotic behavior of a stochastic combustion growth process

Alejandro RamírezVladas Sidoravicius — 2004

Journal of the European Mathematical Society

We study a continuous time growth process on the d -dimensional hypercubic lattice 𝒵 d , which admits a phenomenological interpretation as the combustion reaction A + B 2 A , where A represents heat particles and B inert particles. This process can be described as an interacting particle system in the following way: at time 0 a simple symmetric continuous time random walk of total jump rate one begins to move from the origin of the hypercubic lattice; then, as soon as any random walk visits a site previously...

Uniqueness of invariant product measures for elliptic infinite dimensional diffusions and particle spin systems

Alejandro F. Ramírez — 2002

ESAIM: Probability and Statistics

Consider an infinite dimensional diffusion process process on T 𝐙 d , where T is the circle, defined by the action of its generator L on C 2 ( T 𝐙 d ) local functions as L f ( η ) = i 𝐙 d 1 2 a i 2 f η i 2 + b i f η i . Assume that the coefficients, a i and b i are smooth, bounded, finite range with uniformly bounded second order partial derivatives, that a i is only a function of η i and that inf i , η a i ( η ) > 0 . Suppose ν is an invariant product measure. Then, if ν is the Lebesgue measure or if d = 1 , 2 , it is the unique invariant measure. Furthermore, if ν is translation invariant, then...

Uniqueness of invariant product measures for elliptic infinite dimensional diffusions and particle spin systems

Alejandro F. Ramírez — 2010

ESAIM: Probability and Statistics

Consider an infinite dimensional diffusion process process on , where is the circle, defined by the action of its generator on ) local functions as L f ( η ) = i 𝐙 d 1 2 a i 2 f η i 2 + b i f η i . Assume that the coefficients, and are smooth, bounded, finite range with uniformly bounded second order partial derivatives, that is only a function of η i and that inf i , η a i ( η ) > 0 . Suppose is an invariant product measure. Then, if is the Lebesgue measure or if , it is the unique...

A generalization of a generic theorem in the theory of cardinal invariants of topological spaces

Alejandro Ramírez-PáramoNoé Trinidad Tapia-Bonilla — 2007

Commentationes Mathematicae Universitatis Carolinae

The main goal of this paper is to establish a technical result, which provides an algorithm to prove several cardinal inequalities and relative versions of cardinal inequalities related to the well-known Arhangel’skii’s inequality: If X is a T 2 -space, then | X | 2 L ( X ) χ ( X ) . Moreover, we will show relative versions of three well-known cardinal inequalities.

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