stochastic domination
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2018 ◽  
Vol 50 (01) ◽  
pp. 231-244 ◽  
Author(s):  
Pierre Houdebert

Abstract The continuum random cluster model is a Gibbs modification of the standard Boolean model with intensity z > 0 and law of radii Q. The formal unnormalised density is given by q N cc , where q is a fixed parameter and N cc is the number of connected components in the random structure. We prove for a large class of parameters that percolation occurs for large enough z and does not occur for small enough z. We provide an application to the phase transition of the Widom–Rowlinson model with random radii. Our main tools are stochastic domination properties, a detailed study of the interaction of the model, and a Fortuin–Kasteleyn representation.


2018 ◽  
Vol 53 (2) ◽  
pp. 221-237
Author(s):  
Jacob van den Berg ◽  
Stein Andreas Bethuelsen

2017 ◽  
Vol 6 (2) ◽  
pp. 172 ◽  
Author(s):  
Olubusayo Akinola ◽  
Wen-Hung Kuo ◽  
John Oswald ◽  
Olawunmi Obisesan

This study sought to assess the attitudes of Mental Health Professionals (MHPs) towards tackling illicit drug use and drug-related disorders in Nigeria and to explore regional variations in attitude. Based on the validated Substance Abuse Attitude Survey (SAAS), a quantitative cross-sectional survey was conducted in a randomized sample of 292 MHPs practicing in neuropsychiatric hospitals and mental health departments of teaching hospitals from four geopolitical zones of Nigeria. A response rate of 81.1% was achieved. MHPs tended towards non-permissive, moralistic and stereotypic spectrum and exhibited distinctly defined attitude towards their professional role. The Kruskal-Wallis analysis established significant regional variation in the attitude of multidisciplinary MHPs, <em>H </em>(3)=18.727, <em>p</em>&lt; .0001 reflecting a stochastic domination across the region; therefore a step-down follow-up analysis was conducted. This analysis revealed that the distribution of attitude total-score varies significantly between the South-south and the Southwestern region (<em>p</em>&lt; .0001), the northeastern and southwestern region of the country (<em>p</em>&lt; .028).  A holistic approach towards standardization of drug treatment and care that takes into consideration possible regional variation in attitudes of MHPs should be implemented to foster the reintegration and rehabilitation of drug-using populations into the mainstream society.


2015 ◽  
Vol 98 ◽  
pp. 131-135
Author(s):  
Yuan-Tsung Chang ◽  
William E. Strawderman

2014 ◽  
Vol 36 (2) ◽  
pp. 574-607 ◽  
Author(s):  
RUSSELL LYONS ◽  
ANDREAS THOM

To any positive contraction $Q$ on $\ell ^{2}(W)$, there is associated a determinantal probability measure $\mathbf{P}^{Q}$ on $2^{W}$, where $W$ is a denumerable set. Let ${\rm\Gamma}$ be a countable sofic finitely generated group and $G=({\rm\Gamma},\mathsf{E})$ be a Cayley graph of ${\rm\Gamma}$. We show that if $Q_{1}$ and $Q_{2}$ are two ${\rm\Gamma}$-equivariant positive contractions on $\ell ^{2}({\rm\Gamma})$ or on $\ell ^{2}(\mathsf{E})$ with $Q_{1}\leq Q_{2}$, then there exists a ${\rm\Gamma}$-invariant monotone coupling of the corresponding determinantal probability measures witnessing the stochastic domination $\mathbf{P}^{Q_{1}}\preccurlyeq \mathbf{P}^{Q_{2}}$. In particular, this applies to the wired and free uniform spanning forests, which was known before only when ${\rm\Gamma}$ is residually amenable. In the case of spanning forests, we also give a second more explicit proof, which has the advantage of showing an explicit way to create the free uniform spanning forest as a limit over a sofic approximation. Another consequence of our main result is to prove that all determinantal probability measures $\mathbf{P}^{Q}$ as above are $\bar{d}$-limits of finitely dependent processes. Thus, when ${\rm\Gamma}$ is amenable, $\mathbf{P}^{Q}$ is isomorphic to a Bernoulli shift, which was known before only when ${\rm\Gamma}$ is abelian. We also prove analogous results for sofic unimodular random rooted graphs.


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