In this paper, we prove the hypercontra,ctivity of a non-differentiable Gaussian generalized Mehler semigroup using direct probabilistic argumcents, This result implics the exponential convergence of the scmigroup at ...In this paper, we prove the hypercontra,ctivity of a non-differentiable Gaussian generalized Mehler semigroup using direct probabilistic argumcents, This result implics the exponential convergence of the scmigroup at infinity. Under some additional hypotheses, we also） establish the absolute continuity of the semigroup with respect to its invariant mcasure.展开更多
In this paper,we explore two conjectures about Rademacher sequences.Let(εi)be a Rademacher sequence,i.e.,a sequence of independent{-1,1}-valued symmetric random variables.Set Sn=aiε1+…+anεn for a=(a1,…,an)∈Rn.Th...In this paper,we explore two conjectures about Rademacher sequences.Let(εi)be a Rademacher sequence,i.e.,a sequence of independent{-1,1}-valued symmetric random variables.Set Sn=aiε1+…+anεn for a=(a1,…,an)∈Rn.The first con.jecture says that P(|Sn|≤‖a‖)>1/2 for all a∈Rn and n∈N.The second conjecture says that P(|Sn|>‖a‖)≥7/32 for all a∈Rn and n∈N.Regarding the first conjecture,we present several new equivalent formulations.These include a topological view,a combinatorial version and a strengthened version of the conjecture.Regarding the second conjecture,we prove that it holds true when n<7.展开更多
文摘In this paper, we prove the hypercontra,ctivity of a non-differentiable Gaussian generalized Mehler semigroup using direct probabilistic argumcents, This result implics the exponential convergence of the scmigroup at infinity. Under some additional hypotheses, we also） establish the absolute continuity of the semigroup with respect to its invariant mcasure.
基金supported by the National Natural Science Foundation of China(Nos.11771309,11871184)the China Scholarship Council(No.201809945013)the Natural Sciences and Engineering Research Council of Canada(No.4394-2018)。
文摘In this paper,we explore two conjectures about Rademacher sequences.Let(εi)be a Rademacher sequence,i.e.,a sequence of independent{-1,1}-valued symmetric random variables.Set Sn=aiε1+…+anεn for a=(a1,…,an)∈Rn.The first con.jecture says that P(|Sn|≤‖a‖)>1/2 for all a∈Rn and n∈N.The second conjecture says that P(|Sn|>‖a‖)≥7/32 for all a∈Rn and n∈N.Regarding the first conjecture,we present several new equivalent formulations.These include a topological view,a combinatorial version and a strengthened version of the conjecture.Regarding the second conjecture,we prove that it holds true when n<7.
