<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332021000100079</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v28i1.36294</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Hydrostatic limit for the symmetric exclusion process with long jumps: supper-diffusive case]]></article-title>
<article-title xml:lang="es"><![CDATA[Límite hidroestático para el proceso de exclusión con saltos largos: caso super-difusivo]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Jiménez Oviedo]]></surname>
<given-names><![CDATA[Byron]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ramírez Jiménez]]></surname>
<given-names><![CDATA[Jeremías]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,National University School of Mathematics ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Costa Rica</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,National University School of Mathematics ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Costa Rica</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>07</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>07</month>
<year>2021</year>
</pub-date>
<volume>28</volume>
<numero>1</numero>
<fpage>79</fpage>
<lpage>94</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332021000100079&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332021000100079&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332021000100079&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Hydrostatic behavior for the one dimensional exclusion process with long jumps in contact with infinite reservoirs at different densities are derived. The jump rate is described by a transition probability p which is proportional to | · |&#8722;(&#947;+1) for 1 &lt; &#947; &lt; 2 (supper-diffusive case). The reservoirs add or remove particles with rate proportional to &#954; &gt; 0.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Se deriva el comportamiento hidroestático del proceso de exclusión simple con saltos largos en contacto con depósitos infinitos con diferentes densidades. La tasa de salto es descrita por una función de probabilidad p que es proporcional a | · |&#8722;(&#947;+1) para 1 &lt; &#947; &lt; 2 (caso súperdifusivo). Los depósitos de partículas añaden o retiran partículas con una tasa propocional a &#954; &gt; 0.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[exclusion process with long jumps]]></kwd>
<kwd lng="en"><![CDATA[super-diffusion]]></kwd>
<kwd lng="en"><![CDATA[fractional Fick&#8217;s law.]]></kwd>
<kwd lng="es"><![CDATA[proceso de exclusión con salto largos]]></kwd>
<kwd lng="es"><![CDATA[super-difusión]]></kwd>
<kwd lng="es"><![CDATA[ley de Fick fraccionaria.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[C]]></surname>
<given-names><![CDATA[Bernardin]]></given-names>
</name>
<name>
<surname><![CDATA[P]]></surname>
<given-names><![CDATA[Gonçalves]]></given-names>
</name>
<name>
<surname><![CDATA[B]]></surname>
<given-names><![CDATA[Jiménez-Oviedo.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Slow to fast infinitely extended reservoirs for the symmetric exclusion process with long jumps]]></article-title>
<source><![CDATA[Markov Processes and Related Fields]]></source>
<year>2017</year>
<volume>25</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>217-74</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[C]]></surname>
<given-names><![CDATA[Bernardin]]></given-names>
</name>
<name>
<surname><![CDATA[P]]></surname>
<given-names><![CDATA[Gonçalves]]></given-names>
</name>
<name>
<surname><![CDATA[B]]></surname>
<given-names><![CDATA[Jiménez-Oviedo.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A microscopic model for a one parameter class of fractional Laplacians with Dirichlet boundary conditions]]></article-title>
<source><![CDATA[Archive for Rational Mechanics and Analysis]]></source>
<year>2020</year>
<page-range>1-48</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[C]]></surname>
<given-names><![CDATA[Bernardin]]></given-names>
</name>
<name>
<surname><![CDATA[B]]></surname>
<given-names><![CDATA[Jiménez-Oviedo.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Fractional Fick&#8217;s law for the boundary driven exclusion process with long jumps]]></article-title>
<source><![CDATA[Latin American Journal of Probability and Mathematical Statistics]]></source>
<year>2016</year>
<volume>14</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>473-501</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[P]]></surname>
<given-names><![CDATA[Billingsley.]]></given-names>
</name>
</person-group>
<source><![CDATA[Convergence of Probability Measures]]></source>
<year>2013</year>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[John Wiley &amp; Sons]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Q]]></surname>
<given-names><![CDATA[Guan]]></given-names>
</name>
<name>
<surname><![CDATA[Z]]></surname>
<given-names><![CDATA[Ma.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Reflected symmetric &#945;-stable processes and regional fractional Laplacian]]></article-title>
<source><![CDATA[Probability theory and related fields]]></source>
<year>2005</year>
<volume>134</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>649-94</page-range><publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[C]]></surname>
<given-names><![CDATA[Mou]]></given-names>
</name>
<name>
<surname><![CDATA[Y]]></surname>
<given-names><![CDATA[Yi.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Interior regularity for regional fractional Laplacian]]></article-title>
<source><![CDATA[Communications in Mathematical Physics]]></source>
<year>2015</year>
<volume>340</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>233-51</page-range><publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Vázquez.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators]]></article-title>
<source><![CDATA[Discrete and Continuous Dynamical Systems]]></source>
<year>2014</year>
<volume>7</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>857-85</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
