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To prove Theorem 1.1 we shall combine some classical and rather explicit com- putations of Hasse (concerning Gauss sums) and Leopoldt (concerning integer rings in cyclotomic
In this section, we prove results concerning local (i.e., restricted to proper subspaces) vs global linear dependence of operators that will be used in the proof of Theorem 1.5, and
In this section we define the model of random interlacements in the more general setting of transient weighted graphs and prove the characterization of the process in terms of
We prove a comparison theorem and maximum principle for a local solution of quasi-linear parabolic stochastic PDEs, similar to the well known results in the deterministic case..
We prove the existence and uniqueness of a strong solution of a stochastic differential equation with normal reflection representing the random motion of finitely many globules..
We prove that a stochastic flow of reflected Brownian motions in a smooth multidimensional domain is differentiable with respect to its initial position.. The derivative is a linear
In the next section we transform FB- SDE (1.4) to a stochastic control problem and propose the steepest descent method; in § 3 we discretize the decoupled FBSDEs introduced in § 2;
The results of this section are valid in any dimension d. They describe some essential facts concerning the geometry of the cycles of the energy landscape of the Ising model.
