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A generic elliptic Lagrangian immersion is uniquely determined, up to affine symplectic transformation, by the Fubini cubic
Theorem 1.2. Proof of Theorem 1.1. We will use the following auxiliary results in the proof.. Let SvwT denote the graph obtained from disjoint graphs S, T by adding an edge joining
It is very similar to the proof of Lemma 4 in Kesten (1987), which deals with the probability of four disjoint paths to ∆S(n), two occupied ones and two vacant ones, with the
The integration by parts formula underlies the proof of Lemma 7.1 and is explicitly stated in the simpler setting of first order derivatives in Proposition 8.1.. In [ABBP]
We thank Peter Forrester and Taro Nagao for pointing out the mistake in the proof of lemma 5.6 in (JN06), indicating that terms were missing in the expression for the GUE minor
Applying our proofs to the renewal equation representation (see the proof of their Lemma 2.6), one obtains the same results for local times of Lévy processes as we obtained in
As a corollary thereof, we obtain an integral equation for the modified Laplace transform of the Virgin Island Model in Lemma 5.3 which is the key equation for our proof of
Finally, we note that the proof of the convergence (3) of Theorem 2 (which is given in Section 4) works as it is, when we start the Markov chain with a translation invariant
