Matches in SemOpenAlex for { <https://semopenalex.org/work/W2949068907> ?p ?o ?g. }
Showing items 1 to 99 of
99
with 100 items per page.
- W2949068907 abstract "Consider the stochastic heat equation $partial_t u = (frac{varkappa}{2})Delta u+sigma(u)dot{F}$, where the solution $u:=u_t(x)$ is indexed by $(t,x)in (0, infty)timesR^d$, and $dot{F}$ is a centered Gaussian noise that is white in time and has spatially-correlated coordinates. We analyze the large-$|x|$ fixed-$t$ behavior of the solution $u$ in different regimes, thereby study the effect of noise on the solution in various cases. Among other things, we show that if the spatial correlation function $f$ of the noise is of Riesz type, that is $f(x)propto |x|^{-alpha}$, then the fluctuation exponents of the solution are $psi$ for the spatial variable and $2psi-1$ for the time variable, where $psi:=2/(4-alpha)$. Moreover, these exponent relations hold as long as $alphain(0, dwedge 2)$; that is precisely when Dalang's theory implies the existence of a solution to our stochastic PDE. These findings bolster earlier physical predictions." @default.
- W2949068907 created "2019-06-27" @default.
- W2949068907 creator A5010487903 @default.
- W2949068907 creator A5040696011 @default.
- W2949068907 creator A5053588091 @default.
- W2949068907 creator A5071714134 @default.
- W2949068907 date "2011-11-21" @default.
- W2949068907 modified "2023-10-15" @default.
- W2949068907 title "On the chaotic character of the stochastic heat equation, II" @default.
- W2949068907 cites W1482455015 @default.
- W2949068907 cites W1521233381 @default.
- W2949068907 cites W1828451219 @default.
- W2949068907 cites W1989061230 @default.
- W2949068907 cites W2053481578 @default.
- W2949068907 cites W2068262828 @default.
- W2949068907 cites W2072115074 @default.
- W2949068907 cites W2087496472 @default.
- W2949068907 cites W2127368952 @default.
- W2949068907 cites W2130516017 @default.
- W2949068907 hasPublicationYear "2011" @default.
- W2949068907 type Work @default.
- W2949068907 sameAs 2949068907 @default.
- W2949068907 citedByCount "1" @default.
- W2949068907 crossrefType "posted-content" @default.
- W2949068907 hasAuthorship W2949068907A5010487903 @default.
- W2949068907 hasAuthorship W2949068907A5040696011 @default.
- W2949068907 hasAuthorship W2949068907A5053588091 @default.
- W2949068907 hasAuthorship W2949068907A5071714134 @default.
- W2949068907 hasConcept C105795698 @default.
- W2949068907 hasConcept C112633086 @default.
- W2949068907 hasConcept C114614502 @default.
- W2949068907 hasConcept C115961682 @default.
- W2949068907 hasConcept C121332964 @default.
- W2949068907 hasConcept C134306372 @default.
- W2949068907 hasConcept C138885662 @default.
- W2949068907 hasConcept C14036430 @default.
- W2949068907 hasConcept C154945302 @default.
- W2949068907 hasConcept C163716315 @default.
- W2949068907 hasConcept C182365436 @default.
- W2949068907 hasConcept C202787564 @default.
- W2949068907 hasConcept C2777052490 @default.
- W2949068907 hasConcept C2780388253 @default.
- W2949068907 hasConcept C33923547 @default.
- W2949068907 hasConcept C37914503 @default.
- W2949068907 hasConcept C41008148 @default.
- W2949068907 hasConcept C41895202 @default.
- W2949068907 hasConcept C62520636 @default.
- W2949068907 hasConcept C78458016 @default.
- W2949068907 hasConcept C86803240 @default.
- W2949068907 hasConcept C99498987 @default.
- W2949068907 hasConceptScore W2949068907C105795698 @default.
- W2949068907 hasConceptScore W2949068907C112633086 @default.
- W2949068907 hasConceptScore W2949068907C114614502 @default.
- W2949068907 hasConceptScore W2949068907C115961682 @default.
- W2949068907 hasConceptScore W2949068907C121332964 @default.
- W2949068907 hasConceptScore W2949068907C134306372 @default.
- W2949068907 hasConceptScore W2949068907C138885662 @default.
- W2949068907 hasConceptScore W2949068907C14036430 @default.
- W2949068907 hasConceptScore W2949068907C154945302 @default.
- W2949068907 hasConceptScore W2949068907C163716315 @default.
- W2949068907 hasConceptScore W2949068907C182365436 @default.
- W2949068907 hasConceptScore W2949068907C202787564 @default.
- W2949068907 hasConceptScore W2949068907C2777052490 @default.
- W2949068907 hasConceptScore W2949068907C2780388253 @default.
- W2949068907 hasConceptScore W2949068907C33923547 @default.
- W2949068907 hasConceptScore W2949068907C37914503 @default.
- W2949068907 hasConceptScore W2949068907C41008148 @default.
- W2949068907 hasConceptScore W2949068907C41895202 @default.
- W2949068907 hasConceptScore W2949068907C62520636 @default.
- W2949068907 hasConceptScore W2949068907C78458016 @default.
- W2949068907 hasConceptScore W2949068907C86803240 @default.
- W2949068907 hasConceptScore W2949068907C99498987 @default.
- W2949068907 hasLocation W29490689071 @default.
- W2949068907 hasOpenAccess W2949068907 @default.
- W2949068907 hasPrimaryLocation W29490689071 @default.
- W2949068907 hasRelatedWork W1581308973 @default.
- W2949068907 hasRelatedWork W1988678641 @default.
- W2949068907 hasRelatedWork W2117389153 @default.
- W2949068907 hasRelatedWork W2152750610 @default.
- W2949068907 hasRelatedWork W2805952945 @default.
- W2949068907 hasRelatedWork W2807761617 @default.
- W2949068907 hasRelatedWork W2809714294 @default.
- W2949068907 hasRelatedWork W2906289121 @default.
- W2949068907 hasRelatedWork W2950053065 @default.
- W2949068907 hasRelatedWork W2950191684 @default.
- W2949068907 hasRelatedWork W2952140222 @default.
- W2949068907 hasRelatedWork W3004633268 @default.
- W2949068907 hasRelatedWork W3043949827 @default.
- W2949068907 hasRelatedWork W3092105708 @default.
- W2949068907 hasRelatedWork W3099439462 @default.
- W2949068907 hasRelatedWork W3100559492 @default.
- W2949068907 hasRelatedWork W3104332776 @default.
- W2949068907 hasRelatedWork W3207358329 @default.
- W2949068907 hasRelatedWork W818360428 @default.
- W2949068907 hasRelatedWork W2802737601 @default.
- W2949068907 isParatext "false" @default.
- W2949068907 isRetracted "false" @default.
- W2949068907 magId "2949068907" @default.
- W2949068907 workType "article" @default.