Moyennes uniformes et moyennes suivant une marche aléatoire

Summary Let be a bounded function on such that converges towards l as n goes to infinity, uniformly with respect to m. Let {X _n} be a random walk on , not concentrated on a proper subgroup of Then, with probability 1, converges towards l as n goes to infinity. The result also holds for any countable abelian group instead of . Other modes of convergence are considered (Cesaro convergence of order >1/2). The Cesaro convergence of expressions such that (X _n) (X _n+1) is also investigated.     

Topological hochschild homology of extensions of ?/p? by polynomials, and of ?[x]/(xn) and ?[x]/(xn?1)

Topological Hochschild homology is calculated for the rings /p[x]/(f(x)) (where p is prime and f(x) /p[x] any polynomial), [x]/(x ⁿ) and [x]/(x ⁿ–1). A spectral sequence argument is used for calculating the homology of the topological Hochschild homology spectrum, from which its stable homotopy structure can be read off since the spectrum is known for a priori reasons to be a restricted product of Eilenberg-MacLane spectra.     

Fields with vanishing K2. Torsion in H1(X,K2) and Ch2(x)

This paper describes fields F of nonzero characteristic with the property that for all finite extensions E/F K₂E=0. We consider a somewhat wider class of fields which includes finite and separably closed fields. For smooth projective varieties X over such a field we show that the groups H¹(X, K₂){} and H²(X_et, (2)), NH³(X_et, (2)) and Ch²(X){} are isomorphic. These results are applied to describe the groups SK₁ of a smooth affine curve over such a field.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 116, pp. 108–118, 1982.     

Some Criteria for Multivalently Starlikeness

Let S_n(p)(p, n N) be the class of functions f() = ^p + a_p+n^p+n + which are p-valently starlike in the unit disk. Some sufficient conditions for a function f() to be in the class S_n(p) are given.AMS Subject Classification (2000): primary 30C45     

Compressing Coefficients While Preserving Ideals in K-Theory for C*-Algebras

An invariant based on orderedK-theory with coefficients in _n>1 /n and an infinite number of natural transformations has proved to be necessary and sufficient to classify a large class of nonsimple C* -algebras. In this paper, we expose and explain the relations between the order structure and the ideals of the C* -algebras in question.As an application, we give a new complete invariant for a large class of approximately subhomogeneous C*-algebras. The invariant is based on ordered K-theory with coefficients in /. This invariant is more compact (hence, easier to compute) than the invariant mentioned above, and its use requires computation of only four natural transformations.     

Subdivision algorithms with nonnegative masks generally converge

In this paper, a subdivision scheme consists of an operator froml () tol () determined by a doubly infinite sequence, called the mask. This operator convolutes, in a certain sense, sequences l () with the mask, thus producing a new sequence inl (). Moreover, this new sequence is placed on a finer grid. If we iterate this process with a positive mask infinitely many times, it is known that this process will produce a continuous function, which we callf . In this paper, we consider the extent to which non-negative masks yield similar results. An important application of subdivision schemes in computer graphics is the generation of curves and surfaces from an initial sequence.     

The Eta Invariant and the Connective K-Theory of the Classifying Space for Cyclic 2 Groups

We use the eta invariant to study the connective K-theory groups ko _m (B ) of the classifying space for the cyclic group where - 2 2.     

Almost block independence and bernoullicity of ℤ d -actions by automorphisms of compact abelian groups

Summary We prove that a ^d -action by automorphisms of a compact, abelian group is Bernoulli if and only if it has completely positive entropy. The key ingredients of the proof are the extension of certain notions of asymptotic block independence from -actions to ^d -action and their equivalence with Bernoullicity, and a surprisingly close link between one of these asymptotic block independence properties for ^d -actions by automorphisms of compact, abelian groups and the product formula for valuations on global fields.Oblatum 20-X-1994     

Projective manifolds with the same homology as ℙ k

Complex projective threefolds having the same integral homology groups as ³ are classified. This classification is used to improve a result of Fujita on manifolds whose integral cohomology ring is the same as that of ^k and applies to the problem of classifying polarized manifolds (X, A), A being a nonsingular hypersurface such thatH _i (A, )H _i (X, ) fori2 dimA.Partially supported by M.P.I. of the Italian Government. Both authors are members of G.N.S.A.G.A. of the Italian C.N.R.     

On Localization of Connective Covers

A result of Neisendorfer says that, for every connected p-complete finite complex Y with ₂Y torsion, the p-completion of P_{K(/p, 1)} (Ym) and Y are of the same homotopy type for any positive integer m. Here, P_{K(/p, 1)}(Ym) is the periodization functor of Bousfield and Ym) is the m-connective cover of the space Y. The proof of this result depends on Millers Theorem of Sullivans conjecture. The aim in this paper is to study the phenomenon without the use of Millers Theorem.AMS Subject Classification (2000): 55P60     

Properties of a jointly ergodic action of the direct product of two groups

An ergodic action a of the direct product of and , not isomorphic to a product of actions of and G, is constructed, such that the actions of and G separately are not ergodic. The actions of on its ergodic components are metrically isomorphic if and only if these components are taken into one another by the action of G. Finally, the centralizerC (×G) is such thatC (×G)/(×G)₂.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 5, pp. 684–688, May, 1991.     

Counting Sets With Small Sumset, And The Clique Number Of Random Cayley Graphs

Given a set A /N we may form a Cayley sum graph G _A on vertex set /N by joining i to j if and only if i+j A. We investigate the extent to which performing this construction with a random set A simulates the generation of a random graph, proving that the clique number of G _A is almost surely O(logN). This shows that Cayley sum graphs can furnish good examples of Ramsey graphs. To prove this result we must study the specific structure of set addition on /N. Indeed, we also show that the clique number of a random Cayley sum graph on =(/2) ⁿ is almost surely not O(log ||).* Supported by a grant from the Engineering and Physical Sciences Research Council of the UK and a Fellowship of Trinity College Cambridge.     

Some mildly wild circles in Sn arising from algebraic K-Theory

We study wild embeddings of S ¹ in S ⁿ which are tame in a sense introduced by Quinn. We show that if is a finitely presented group with H ₁()=H ₂()=0, then any finiteness obstruction K ₀() can be realized on the complement of such an embedded S ¹. We also realize trivially symmetric K _–1() obstructions on the complements of such embeddings. For trivially symmetric , the embeddings constructed are shown to be isotopy homogeneous.     

ApproximatingK*(?) through degree five

We approximate theK-theory spectrum of the integers using a spectrum level rank filtration. By means of a certain poset spectral sequence, we explicitly compute the first three subquotients of this filtration. Assuming a conjecture about the filtration's rate of convergence, we conclude thatK ₄()=0 andK ₅() is a copy of (the Borel summand) plus two-torsion of order at most eight.     

On a Theorem of Grothendieck

A smooth projective morphism p : T S to a smooth variety S is considered. In particular, the following result is proved. The total direct image Rp _*(/n) of the constant étale sheaf /n is locally (in Zariski topology) quasiisomorphic to a bounded complex on S that consists of locally constant, constructible étale sheaves of /n-modules. Bibliography: 2 titles.     

Central Limit Theorem for a Class of Nonhomogeneous Random Walks

A spatially nonhomogeneous random walk _t on the grid =^m X ⁿ is considered. Let _t ⁰ be a random walk homogeneous in time and space, and let _t be obtained from it by changing transition probabilities on the set A= X ⁿ, || < , so that the walk remains homogeneous only with respect to the subgroup ⁿ of the group . It is shown that if >m 2 or the drift is distinct from zero, then the central limit theorem holds for _t.     

First passage percolation: The stationary case

Summary If the passage time of the edges of the ^d lattice are stationary, ergodic and have finite moment of orderp>d, then a.s. the set of vertices that can be reached within timet, has an asymptotic shape ast.     

Eisenstein Cohomology and the Construction of p-Adic Analytic L-Functions

Let be a cuspidal automorphic representation of GL₃( ), unramified at pand of cohomological type at infinity. We construct p-adic L-functions, which interpolate the critical values of L(,s) and which satisfy a logarithmic growth condition. We obtain these functions as p-adic Mellin transforms of certain distributions on _p ^* having values in some fixed number field and which are of moderate growth. In the p-ordinary case we obtain the bound |(U)| _p |_Haar(U)| _p for open subsets U _p ^*, where _Haardenotes the invariant distribution on _p ^*.     

A necessary condition forB-convergence of Runge-Kutta methods

Algebraic stability is a well-known property necessary forB-convergence of a Runge-Kutta method, provided its nodesc _i are such thatc _i – c _j wheneveri j. In this paper a slightly weaker property is established which becomes algebraic stability as soon asc _i – c _j , wheneveri j is excluded.Using this condition it is shown that the Lobatto IIIA methods with more than two stages cannot beB-convergent.This paper was written while the author was visiting the Rijksuniversiteit Leiden in the Netherlands, supported by the Netherlands Organization for Scientific Research (N.W.O.) and by an Erwin Schrödinger scholarship from the Fonds zur Förderung der wissenschaftlichen Forschung.     

Processus des misanthropes

Summary We consider a system of identical interacting particles moving on the lattice ^d . The rate at which a particle at the site x jumps to the site y is p(y–x)b((x), (y)) where p is an irreducible probability on ^d and b((x), (y)) is an increasing (resp. decreasing) function of the number (x) (resp. (y)) of particles at site x (resp. y). We study the convergence of the system to equilibrium and describe the invariant measures.