相关论文: Descent equalities and the inductive McKay conditi…

We consider branching random walks with a spine in the domain of attraction of an $\alpha$-stable L\'evy process. For this process, the classical derivative martingale in general degenerates in the limit. We first determine the quantity…

A sufficient condition for the simplicity of induced modules of reductive Lie algebras is given.

We show that the natural stratifications arising from certain deformation families of line singularities with constant L\^e numbers satisfy Bekka's $(c)$-regularity condition. As a corollary, we obtain that these families are topologically…

We consider II$_1$ factors $M$ which can be realized as inductive limits of subfactors, $N_n \nearrow M$, having spectral gap in $M$ and satisfying the bi-commutant condition $(N_n'\cap M)'\cap M=N_n$. Examples are the enveloping algebras…

We prove estimates for $\mathbb{E} \| X: \ell_{p'}^n \to \ell_q^m\|$ for $p,q\ge 2$ and any random matrix $X$ having the entries of the form $a_{ij}Y_{ij}$, where $Y=(Y_{ij})_{1\le i\le m, 1\le j\le n}$ has i.i.d. isotropic log-concave…

We study identifiability for bilinear inverse problems under sparsity and subspace constraints. We show that, up to a global scaling ambiguity, almost all such maps are injective on the set of pairs of sparse vectors if the number of…

A general nonlinear regularity model for a set-valued mapping $F:X\times R_+\rightrightarrows Y$, where $X$ and $Y$ are metric spaces, is considered using special iteration procedures, going back to Banach, Schauder, Lusternik and Graves.…

We give new criteria for the irreducibility of parabolic induction on the general linear group and its inner forms over a local non-archimedean field. In particular, we give a necessary and sufficient condition when the inducing data is of…

In this paper we study the exponential decay of posterior probability of a set of sources and conditioning by rare sources for both uniform and general prior distributions of sources. The decay rate is determined by $L$-divergence and rare…

We provide an amendment to the first theorem of "Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design" by Manchester & Slotine in the form of an additional technical condition required to show…

We give a new moduli construction of the minimal resolution of the singularity of type 1/r(1,a) by introducing the Special McKay quiver. To demonstrate that our construction trumps that of the G-Hilbert scheme, we show that the induced…

We construct the law of L\'{e}vy processes conditioned to stay positive under general hypotheses. We obtain a Williams type path decomposition at the minimum of these processes. This result is then applied to prove the weak convergence of…

Finite determinacy for mappings has been classically thoroughly studied in numerous scenarios in the real- and complex-analytic category and in the differentiable case. It means that the map-germ is determined, up to a given equivalence…

We work towards a version of generalized Harish-Chandra theory compatible with Clifford theory and with the action of automorphisms on irreducible characters. This provides a fundamental tool to verify the inductive conditions for the…

Necessary and sufficient conditions are given for the Palais-Smale Condition C to hold for the Yang-Mills functional for connections that are invariant under a Lie group action on the manifold with orbits of codimension less than or equal…

In this article, we shall start with a closed walk on a regular tree of degree $d$. These walks are described by the Kesten-McKay law which arises as the asymptotic distribution of a random $d$-regular graph on $n$ vertices. We will show…

It is common to model inductive datatypes as least fixed points of functors. We show that within the Cedille type theory we can relax functoriality constraints and generically derive an induction principle for Mendler-style lambda-encoded…

In this note, notwithstanding the generalization, we simplify and shorten the proofs of the main results of the third author's paper \cite{SXY} significantly. In particular, the new proof for \cite[Theorem 1.1]{SXY} is quite short and,…

This paper proposes a way of doing type theory informally, assuming a cubical style of reasoning. It can thus be viewed as a first step toward a cubical alternative to the program of informalization of type theory carried out in the…

It is a basic fact in infinite-dimensional Lie theory that the unit group G(A) of a continuous inverse algebra A is a Lie group. We describe criteria ensuring that the Lie group G(A) is regular in Milnor's sense. Notably, G(A) is regular if…