Journal of the London Mathematical Society-Second Series最新文献

In this paper, we give a local estimate for the Kobayashi distance on a bounded convex domain of finite type, which relates to a local pseudodistance near the boundary. The estimate is precise up to a bounded additive term. Also, we conclude that the domain equipped with the Kobayashi distance is Gromov hyperbolic that gives another proof of the result of Zimmer.

We prove that applying a projective functor to a holonomic simple module over a semisimple finite-dimensional complex Lie algebra produces a module that has an essential semisimple submodule of finite length. This implies that holonomic simple supermodules over certain Lie superalgebras are quotients of modules that are induced from simple modules over the even part. We also provide some further insight into the structure of Lie algebra modules that are obtained by applying projective functors to simple modules.

Let $�M$ be a semifinite von Neumann algebra equipped with an increasing filtration $�{�\left(�M_n�\right)�}_{�n�⩾�1�}$ of (semifinite) von Neumann subalgebras of $�M$. For $��1�⩽�p�⩽�\infty �$, let $��H_p^c��\left(�M�\right)��$ denote the noncommutative column martingale Hardy space constructed from column square functions associated with the filtration $�{�\left(�M_n�\right)�}_{�n�⩾�1�}$ and the index $�p$. We prove the following real interpolation identity: If $��0�<�\theta �<�1�$

The subrank of a tensor measures how much a tensor can be diagonalized. We determine this parameter precisely for essentially all (i.e., generic) tensors. Namely, we prove for generic tensors in $��V�\otimes �V�\otimes �V�$ with $��dim�\left(�V�\right)�=�n�$ that the subrank is $��\Theta �\left(�\sqrt{�n�}�\right)�$. Our result significantly improves on the previous upper bound from the work of Strassen (1991) and Bürgisser (1990) which was $�n^{�2�/�3�+�o�\left(�1�\right)�}$. Our result is tight up to an additive constant. Our full result covers not only 3-tensors but also $�k$-tensors, for which we find that the generic subrank is $��\Theta �\left(�n^{�1�/�(�k�-�1�)�}�\right)�$

Let $��N�>�1�$ be an integer coprime to 6 such that $��N�\notin �\{�5�,�7�,�13�\}�$ and let $��g�=�g�\left(�N�\right)�$ be the genus of the modular curve $��X_0��\left(�N�\right)��$. We compute the intersection matrices relative to special fibres of the minimal regular model of $��X_0��\left(�N�\right)��$. Moreover, we prove that the self-intersection of the Arakelov canonical sheaf of $��X_0��\left(�N�\right)��$ is asymptotic to $��3�g�\log �N�$, for $��$

A theorem of Llarull says that if a smooth metric $�g$ on the $�n$-sphere $�S^n$ is bounded below by the standard round metric and the scalar curvature $�R_g$ of $�g$ is bounded below by $��n�(�n�-�1�)�$, then the metric $�g$ must be the standard round metric. We prove a spectral Llarull theorem by replacing the bound $��R_g�⩾�n��(�n�-�1�)��$ by a lower bound on the first eigenvalue of an elliptic operator involving the Laplacian and the scalar curvature $�R_g$. We utilize two methods: spinor and spacetime harmonic function.

Eigenvalues of Wigner matrices has been a major topic of investigation. A particularly important subclass of such random matrices, useful in many applications, are what are known as sparse or diluted random matrices, where each entry in a Wigner matrix is multiplied by an independent Bernoulli random variable with mean $�p$. Alternatively, such a matrix can be viewed as the adjacency matrix of an Erdős–Rényi graph $�G_{�n�,�p�}$ equipped with independent and identically distributed (i.i.d.) edge-weights. An observable of particular interest is the largest eigenvalue. In this paper, we study the large deviations behavior of the largest eigenvalue of such matrices, a topic that has received considerable attention over the years. While certain techniques have been devised for the case when $�p$ is fixed or perhaps going to zero not too fast with the matrix size, we focus on the case $��p�=�\frac{d}{n}�$, that is, constant average degree regime of sparsity, which is a central example due to its connections to many models in statistical mechanics and other applications. Most known techniques break down in this regime and even the typical behavior of the spectrum of such random matrices is not very well understood. So far, results were known only for the Erdős–Rényi graph $�G_{�n�,�\frac{d}{n}�}$ without edge-weights and with Gaussian edge-weights. In the present article, we consider the effect of general weight distributions. More specifically, we consider entry distributions whose tail probabilities decay at rate $�$

In this paper, I introduce the properties $�{\mathrm{EPC}}_{{\aleph }_1}$ and $��\mathrm{ProjCes}�\left(�E�\right)�$ for forcing notions and show that it is consistent that the forcing axiom for $��{\mathrm{EPC}}_{{\aleph }_1}�+�\mathrm{ProjCes}��\left(�E�\right)��$ forcing notions holds, the continuum hypothesis fails, and an ultrapower of the field of reals has the property $�{\beta }_1$. This provides a partial solution to H. Woodin's question concerning the existence of discontinuous homomorphisms on the Banach algebra of all complex-valued continuous functions on a compact space. Furthermore, we prove that the uniformization of a coloring of a ladder system on a stationary–costationary set $�E$ is an example of an $��{\mathrm{EPC}}_{{\aleph }_1}�+�\mathrm{ProjCes}��(�{\omega }_1�\setminus �E�)��$