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Incidentally, note that a corollary of Theorem 3.1 (see the corollary below) allows the elegant solution of classical problems of analytical geometry, such as finding the parametric
Large deviation principles are established for the two-parameter Poisson-Dirichlet distribu- tion and two-parameter Dirichlet process when parameter θ approaches infinity. The
Since no two collisions occur simultaneously, the number of collisions C n in the Λ-coalescent starting with n particles is the number of steps the Markov chain M n needs to
Combining Theorem 7, the tensorization property of Beckner type-inequalities, Corollary 8 and Theorem 12 allows to derive dimension-free isoperimetric inequalities for the products
In [ NSV1 ] , Nazarov, Sodin and Volberg also noticed that t-dilation is well suited for sublevel sets of functions satisfying a Remez type inequality and deduced from the
When all demes are connected by fast migration, they show that structured genealogy collapses to an unstructured Kingman’s coalescent as N tends to in- finity, due to the fact
Corollary 4.4 of the present paper (specialised to the case J = 2) establishes strong uniqueness and existence of associated reflected diffusions (with drift and diffusion
As a direct corollary of our results, a Dunkl harmonic function bounded below or above is actually constant, which extends the corresponding result of Gallardo and Godefroy for
