Dalang, Robert C.Mueller, CarlXiao, Yimin2021-10-092021-10-092021-10-092021-09-0110.1214/21-AOP1516https://infoscience.epfl.ch/handle/20.500.14299/182026WOS:000700613800012We study vector-valued solutions u(t, x) is an element of R-d to systems of nonlinear stochastic heat equations with multiplicative noise,partial derivative/partial derivative t u(t, x) = partial derivative(2)/partial derivative x(2) u(t, x) + sigma (u(t, x)(W) over dot (t, x).Here, t >= 0, x is an element of R and (W) over dot (t, x) is an R-d-valued space-time white noise. We say that a point z is an element of R-d is polar ifP{u(t, x) = z for some t > 0 and x is an element of R} = 0.We show that, in the critical dimension d = 6, almost all points in R-d are polar.Statistics & ProbabilityMathematicshitting probabilitiespolarity of pointscritical dimensionnonlinear stochastic partial differential equationstrajectoriestext::journal::journal article::research article