Related papers: A view from infinity of the uniform infinite plana…
In this paper we study the theories of the infinite-branching tree and the $r$-regular tree, and show that both of them are pseudofinite. Moreover, we show that they can be realized by infinite ultraproducts of polynomial exact classes of…
We introduce an infinite set of integer mappings that generalize the well-known Collatz-Ulam mapping and we conjecture that an infinite subset of these mappings feature the remarkable property of the Collatz conjecture, namely that they…
The paper deals with the solution of Shevrin ans Sapir problem. Infinite finitely presented nilsemigroup is constructed. The construction is based on aperiodic tilings, Goodman-Strauss type theorems on uniformly elliptic space. Space is…
A new generalized formulation of the spectral condition is proposed for quantum fields with highly singular infrared behavior whose vacuum correlation functions are well defined only under smearing with analytic test functions in momentum…
We study how iterated and composed completely positive maps act on operator-valued kernels. Each kernel is realized inside a single Hilbert space where composition corresponds to applying bounded creation operators to feature vectors. This…
Let $p$ and $q$ be anisotropic quasilinear quadratic forms over a field $F$ of characteristic $2$, and let $i$ be the isotropy index of $q$ after scalar extension to the function field of the affine quadric with equation $p=0$. In this…
We find a countable partition $P$ on\textbf{} a Lebesgue space, labeled $\{1,2,3...$\}, for any non-periodic measure preserving transformation $T$ such that $P$ generates $T$ and for the $T,P$ process, if you see an $n$ on time -1 then you…
We introduce a growth process which samples sections of uniform infinite causal triangulations by elementary moves in which a single triangle is added. A relation to a random walk on the integer half line is shown. This relation is used to…
We study compact K\"ahler threefolds X with infinite fundamental group whose universal cover can be compactified. Combining techniques from $L^2$ -theory, Campana's geometric orbifolds and the minimal model program we show that this…
We introduce the notion of a lowering-raising (or LR) triple of linear transformations on a nonzero finite-dimensional vector space. We show how to normalize an LR triple, and classify up to isomorphism the normalized LR triples. We…
The Kruskal-Friedman theorem asserts: in any infinite sequence of finite trees with ordinal labels, some tree can be embedded into a later one, by an embedding that respects a certain gap condition. This strengthening of the original…
We characterize the variety of compatible fundamental matrix triples by computing its multidegree and multihomogeneous vanishing ideal. This answers the first interesting case of a question recently posed by Br{\aa}telund and Rydell. Our…
The present work stemmed from the study of the problem of harmonic analysis on the infinite-dimensional unitary group U(\infty). That problem consisted in the decomposition of a certain 4-parameter family of unitary representations, which…
We prove sandwich theorems and a Tauberian theorem in the space of compact metric measure spaces, endowed with the Gromov-Hausdorff-Prokhorov (GHP) topology. These results hold with respect to a close relative of Gromov's Lipschitz order.…
We prove that the problem of constructing biharmonic conformal maps on a $4$-dimensional Einstein manifold reduces to a Yamabe-type equation. This allows us to construct an infinite family of examples on the Euclidean 4-sphere. In addition,…
In earlier work, we constructed invariants of irreducible representations of the Kauffman skein algebra of a surface. We introduce here an inverse construction, which to a set of possible invariants associates an irreducible representation…
Generalising an example by Girondo and Wolfart, we use finite group theory to construct Riemann surfaces admitting two or more regular dessins (i.e. orientably regular hypermaps) with automorphism groups of the same order, and in many cases…
We prove that the free uniform spanning forest of any bounded degree proper plane graph is connected almost surely, answering a question of Benjamini, Lyons, Peres and Schramm. We provide a quantitative form of this result, calculating the…
Via circle pattern techniques, random planar triangulations (with angle variables) are mapped onto Delaunay triangulations in the complex plane. The uniform measure on triangulations is mapped onto a conformally invariant spatial point…
The Urysohn space is a complete separable metric space, universal among separable metric spaces for extending finite partial isometries into it. We present an alternative construction of the Urysohn space which enables us to show that…