(Non)-escape of mass and equidistribution for horospherical actions on trees

Let G be a large group acting on a biregular tree T and $$\Gamma \le G$$ Γ ≤ G a geometrically finite lattice. In an earlier work, the authors classified orbit closures of the action of the horospherical subgroups on $$G/\Gamma $$ G / Γ . In this article we show that there is no escape of mass and use this to prove that, in fact, dense orbits equidistribute to the Haar measure on $$G/\Gamma $$ G / Γ . On the other hand, we show that new dynamical phenomena for horospherical actions appear on quotients by non-geometrically finite lattices: we give examples of non-geometrically finite lattices where an escape of mass phenomenon occurs and where the orbital averages along a Følner sequence do not converge. In the last part, as a by-product of our methods, we show that projections to $$\Gamma \backslash T$$ Γ \ T of the uniform distributions on large spheres in the tree T converge to a natural probability measure on $$\Gamma \backslash T$$ Γ \ T . Finally, we apply this equidistribution result to a lattice point counting problem to obtain counting asymptotics with exponential error term.

An Efficient Approach to Point-Counting on Elliptic Curves from a Prominent Family over the Prime Field Fp

Here, we elaborate an approach for determining the number of points on elliptic curves from the family Ep={Ea:y2=x3+a(modp),a≠0}, where p is a prime number >3. The essence of this approach consists in combining the well-known Hasse bound with an explicit formula for the quantities of interest-reduced modulo p. It allows to advance an efficient technique to compute the six cardinalities associated with the family Ep, for p≡1(mod3), whose complexity is O˜(log2p), thus improving the best-known algorithmic solution with almost an order of magnitude.

Supplemental Material: Reconstructing the tectono-sedimentary evolution of the Early–Middle Jurassic Tlaxiaco Basin in southern Mexico: New insights into the crustal attenuation history of southern North America during Pangea breakup

<div>File A: Point-counting raw data and recalculated parameters for whole-rock sandstone petrography. File B: Details of analytical methodology and analytical results for individual zircon ages. <br></div>

Supplemental Material: Reconstructing the tectono-sedimentary evolution of the Early–Middle Jurassic Tlaxiaco Basin in southern Mexico: New insights into the crustal attenuation history of southern North America during Pangea breakup

<div>File A: Point-counting raw data and recalculated parameters for whole-rock sandstone petrography. File B: Details of analytical methodology and analytical results for individual zircon ages. <br></div>

The bead process for beta ensembles

The bead process introduced by Boutillier is a countable interlacing of the $${\text {Sine}}_2$$ Sine 2 point processes. We construct the bead process for general $${\text {Sine}}_{\beta }$$ Sine β processes as an infinite dimensional Markov chain whose transition mechanism is explicitly described. We show that this process is the microscopic scaling limit in the bulk of the Hermite $$\beta $$ β corner process introduced by Gorin and Shkolnikov, generalizing the process of the minors of the Gaussian Unitary and Orthogonal Ensembles. In order to prove our results, we use bounds on the variance of the point counting of the circular and the Gaussian beta ensembles, proven in a companion paper (Najnudel and Virág in Some estimates on the point counting of the Circular and the Gaussian Beta Ensemble, 2019).

A simple, effective petrographic method for quantifying percent clay or other grain-coat coverage in sandstones

ABSTRACT A simple petrographic method is presented to quantify the percent of grain-coat coverage in sandstones. The method involves visually noting whether, at the intersection of a grain boundary and an ocular crosshair, a grain coat (or other grain coating) is present or absent. If a coating is absent at the juncture of the grain boundary and the ocular crosshair, then it can be recorded whether an open pore, a pore-filling cement, or another grain is present at that point. The technique is simple to apply as part of standard point-counting procedures for composition or for grain size. It is much less time consuming, minutes rather than hours, than methods that involve measuring grain perimeters and grain-coat length on SEM images or on thin sections. Computer simulations and comparative measurements on sets of the same samples suggest that they yield results comparable to those techniques. It is less subjective than visual estimates of grain-coat coverage and gives more reproducible results. The mineralogy of the grain coat, its thickness, and its paragenetic relationships to other grain-coating phases can be simultaneously recorded.