90 research outputs found
On the time schedule of Brownian Flights
We are interested on the statistics of the duration of Brownian diffusions
started at distance \epsilon from a given boundary and stopped when they hit
back the interface.Comment: 9 page
Carleson measures and chord-arc curves
Following Semmes and Zinsmeister, we continue the study of Carleson measures
and their invariance under pull-back and push-forward operators. We also study
the analogous statements for vanishing Carleson measures. As an application, we
show that some quotient space of the space of chord-arc curves has a natural
complex structure.Comment: 21 page
On the Hausdorff dimension of Julia sets of some real polynomials
We show that the supremum for real of the Hausdorff dimension of the
Julia set of the polynomial ( is an even natural number) is
greater than .Comment: 10 page, 4 figure
Variations of Hausdorff Dimension in the Exponential Family
In this paper we deal with the following family of exponential maps
. Denoting
the hyperbolic dimension of . It is known that the
function is real analytic in , and
that it is continuous in . In this paper we prove that this map is
C on , with . Moreover, depending on the value of
, we give estimates of the speed of convergence towards 0.Comment: 32 pages. A para\^itre dans Annales Academi{\ae} Scientiarum
Fennic{\ae} Mathematic
On The Brownian Loop Measure
In 2003 Lawler and Werner introduced the Brownian loop measure and studied
some of its properties. Cardy and Gamsa has predicted a formula for the total
mass of the Brownian loop measure on the set of simple loops in the upper half
plane and disconnect two given points from the boundary. In this paper we give
a rigorous proof of the formula using a result by Beliaev and Viklund and heavy
computations.Comment: 19 page
Integral means spectrum of whole-plane SLE
We complete the mathematical analysis of the fine structure of harmonic
measure on SLE curves that was initiated by Beliaev and Smirnov, as described
by the averaged integral means spectrum. For the unbounded version of
whole-plane SLE as studied by Duplantier, Nguyen, Nguyen and Zinsmeister, and
Loutsenko and Yermolayeva, a phase transition has been shown to occur for high
enough moments from the bulk spectrum towards a novel spectrum related to the
point at infinity. For the bounded version of whole-plane SLE studied here, a
similar transition phenomenon, now associated with the SLE origin, is proved to
exist for low enough moments, but we show that it is superseded by the earlier
occurrence of the transition to the SLE tip spectrum.Comment: 14 pages, 1 figure; final versio
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