Bulletin of the London Mathematical Society最新文献

This paper proves the existence of a chiral map with alternating automorphism group for every hyperbolic type. Equivalently, for every pair of natural numbers $��(�m�,�n�)�$ such that , there is a finite alternating group generated by a pair of elements whose orders are $�m$ and $�n$ and whose product is an involution, where furthermore the group does not have an automorphism which inverts these generators. We call on previously known results for when both the valency $�n$ and the face-length $�m$ are odd, and present a set of new constructions using permutations for when at least one parameter is even.

The purpose of this paper is to establish a connection between a one-dimensional random walk in a random sparse environment and the random pinning model. We show that the grand canonical partition function of the pinning model coincides with the mean number of returns to the origin for a random walk in a random sparse environment averaged over the randomness location. We obtain thereof some information on the integrability of the number of return times in the annealed and partially annealed setups.

For any given set $��E�\subset �[�1�,�2�]�$, we discuss a fractal frequency-localized version of the $�L^p$ local smoothing estimates for the half-wave propagator with times in $�E$. A conjecture is formulated in terms of a quantity involving the Assouad spectrum of $�E$ and the Legendre transform. We validate the conjecture for radial functions. We also prove a similar result for fractal-time $��L^2�\to �L^q�$ and square function bounds, for arbitrary $�L^2$ functions and general time sets. We formulate a conjecture for $��L^p�\to �L^q�$ generalizations.

Stable envelopes, introduced by Maulik and Okounkov, provide a family of bases for the equivariant cohomology of symplectic resolutions. They are part of a fascinating interplay between geometry, combinatorics and integrable systems. In this expository article, we give a self-contained introduction to cohomological stable envelopes of type $�A$ bow varieties. Our main focus is on the existence and the orthogonality properties of stable envelopes for bow varieties. The restriction to this specific class of varieties allows us to illustrate the theory combinatorially and to provide simplified proofs, both laying a basis for explicit calculations.

We give an unconditional proof of the Coba conjecture for wonderful compactifications of adjoint type for semisimple Lie groups of type $�A_n$. We also give a proof of a slightly weaker conjecture for wonderful compactifications of adjoint type for arbitrary Lie groups.

We define the orbit morphism of partial dynamical systems and prove that an orbit morphism being an isomorphism in the category of partial dynamical systems and orbit morphisms is equivalent to the existence of a continuous orbit equivalence between the given partial dynamical systems that preserves the essential stabilisers. We show that this is equivalent to the existence of a diagonal-preserving isomorphism between the corresponding crossed products when the essential stabilisers of partial actions are torsion-free and abelian. We also characterise when an étale groupoid is isomorphic to the transformation groupoid of some partial action. Additionally, we explore the implications in the context of semi-saturated orthogonal partial dynamical systems over free groups, establishing connections with Deaconu–Renault systems and the concept of eventual conjugacy.

This paper is concerned with random holomorphic functions over the infinite-dimensional polydisc. The celebrated Billard's theorem states, among other things, that for a random holomorphic function in a single variable—obtained by placing a random sign before each Taylor coefficient—the boundedness of the function can be automatically improved to continuity. We extend Billard's theorem in three aspects: first, we extend it to the case of infinitely many variables. Second, we establish an inverse result, that is, not merely a sufficient condition. Such results are rare in the literature. In particular, we define Billard's property (BP) for random variables and prove: (1) all symmetric random variables have BP; (2) a square-integrable random variable has BP if and only if it is centered. Third, another novelty of our results is that they encompass applications to random Dirichlet series.

Complementing our previous results, we give a classification of all isometries (not necessarily surjective) of the metric space consisting of ball-bodies, endowed with the Hausdorff metric. ‘Ball-bodies’ are convex bodies which are intersections of translates of the Euclidean unit ball. We show that any such isometry is either a rigid motion or a rigid motion composed of the $�c$-duality mapping. In particular, any isometry on this metric space has to be surjective.

We show that the complex of partial bases of the free group of rank $�n$, where vertices are seen up to conjugation, is Cohen–Macaulay of dimension $��n�-�1�$. This confirms a conjecture by Day and Putman. We prove our results in the more general context of freely decomposable groups.