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We prove that the Hausdorff dimension of the set of badly approximable systems of m linear forms in n variables over the field of Laurent series with coefficients from a finite field
The knowledge of the contact graphs of these substitutions enables us to establish an explicit formula for the Hausdorff dimension of the boundary of the associated Rauzy fractals
Lemma 3.2 in Dinwoodie and Zabell (1992) gives conditions under which uni-tight holds when, for each θ, P n.. θ is the distribution (on a rather general space) of the average
We prove that the Hausdorff dimension of the frontier equals 2(1 − α ) where α is an exponent for Brownian motion called the two-sided disconnection exponent.. In particular, using
The proof of this lemma would follow by the same arguments as the proof of Lemma 3.1 of [5], applying the criterion for absolute continuity of the supremum of a Gaussian
Thus, Corollary 3 states that the process of departures from the queue has the same law as the process of arrivals to the queue; it can therefore be regarded as an extension of
In this section, we use Corollary 2 to determine whether the Λ-coalescent comes down from infinity for particular families of measures Λ. We begin with the
The following lemma gives a lower bound on the range of a random homomorphism of C n,k with exactly ℓ non-constant layers.
