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Let $Γ$ be a group endowed with a length function $L$ , and let $E$ be a linear subspace of $C Γ$ . We say that $E$ satisfies the Haagerup inequality if there exists constants $C, s > 0$ such that, for any $f \in E$ , the convolutor norm of $f$ on $ℓ^{2} (Γ)$ is dominated by $C$ times the $ℓ^{2}$ norm of $f (1 + L)^{s}$ . We show that, for $E = C Γ$ , the Haagerup inequality can be expressed in terms of decay of random walks associated with finitely supported symmetric probability measures on $Γ$ . If $L$ is a word length function on a finitely generated group $Γ$ , we show that,...

On the invariant measure of the random difference equation Xn = AnXn−1 + Bn in the critical case

Sara Brofferio, Dariusz Buraczewski, Ewa Damek (2012)

Annales de l'I.H.P. Probabilités et statistiques

We consider the autoregressive model on ℝd defined by the stochastic recursion Xn = AnXn−1 + Bn, where {(Bn, An)} are i.i.d. random variables valued in ℝd× ℝ+. The critical case, when $𝔼 [log A_{1}] = 0$ , was studied by Babillot, Bougerol and Elie, who proved that there exists a unique invariant Radon measureν for the Markov chain {Xn}. In the present paper we prove that the weak limit of properly dilated measure ν exists and defines a homogeneous measure on ℝd ∖ {0}.

On the law of the iterated logarithm for increments of sums of independent random variables.

Frolov, A.N. (2004)

Zapiski Nauchnykh Seminarov POMI

On the limit behaviour of sums of a random number of independent random variables

Z. Rychlik, D. Szynal (1973)

Colloquium Mathematicae

On the limit distribution of the well-distribution measure of random binary sequences

Christoph Aistleitner (2013)

Journal de Théorie des Nombres de Bordeaux

We prove the existence of a limit distribution of the normalized well-distribution measure $W (E_{N}) / \sqrt{N}$ (as $N \to \infty$ ) for random binary sequences $E_{N}$ , by this means solving a problem posed by Alon, Kohayakawa, Mauduit, Moreira and Rödl.

On the limiting velocity of random walks in mixing random environment

Xiaoqin Guo (2014)

Annales de l'I.H.P. Probabilités et statistiques

We consider random walks in strong-mixing random Gibbsian environments in $ℤ^{d}$ , $d \geq 2$ . Based on regeneration arguments, we will first provide an alternative proof of Rassoul-Agha’s conditional law of large numbers (CLLN) for mixing environment (Electron. Commun. Probab.10(2005) 36–44). Then, using coupling techniques, we show that there is at most one nonzero limiting velocity in high dimensions ( $d \geq 5$ ).

On the Maximum of a Branching Process Conditioned on the Total Progeny

Kerbashev, Tzvetozar (1999)

Serdica Mathematical Journal

The maximum M of a critical Bienaymé-Galton-Watson process conditioned on the total progeny N is studied. Imbedding of the process in a random walk is used. A limit theorem for the distribution of M as N → ∞ is proved. The result is trasferred to the non-critical processes. A corollary for the maximal strata of a random rooted labeled tree is obtained.

On the moments of hitting times for random walks on trees.

Palacios, José Luis (2009)

Journal of Probability and Statistics

On the norms of the random walks on planar graphs

Andrzej Żuk (1997)

Annales de l'institut Fourier

We consider the nearest neighbor random walk on planar graphs. For certain families of these graphs, we give explicit upper bounds on the norm of the random walk operator in terms of the minimal number of edges at each vertex. We show that for a wide range of planar graphs the spectral radius of the random walk is less than one.

On the number of representations of an element in a polygonal Cayley graph

Gabriella Kuhn, Paolo M. Soardi (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We compute explicitly the number of paths of given length joining two vertices of the Cayley graph of the free product of cyclic groups of order k.

Upper estimates are presented for the universal constant in the Katz-Petrov and Osipov inequalities which do not exceed 3.1905.

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On the distribution density of the supremum of a random walk in the subexponential case.

On the distribution of random walk local time

On the domination of a random walk on a discrete cylinder by random interlacements.

On the exact distributional asymptotics for the supremum of a random walk with increments in a class of light-tailed distribution.

On the fixed point index of non-compact mappings

On the Haagerup inequality and groups acting on ${\tilde{A}}_{n}$ -buildings

On the invariant measure of the random difference equation Xn = AnXn−1 + Bn in the critical case

On the law of the iterated logarithm for increments of sums of independent random variables.

On the limit behaviour of sums of a random number of independent random variables

On the limit distribution of the well-distribution measure of random binary sequences

On the limiting velocity of random walks in mixing random environment

On the Maximum of a Branching Process Conditioned on the Total Progeny

On the moments of hitting times for random walks on trees.

On the norms of the random walks on planar graphs

On the number of representations of an element in a polygonal Cayley graph

On the order of growth of convergent series of independent random variables.

On the sample path behavior of the first passage time process of a brownian motion with drift

On the shuffling algorithm for domino tilings.

On the speed of a planar random walk avoiding its past convex hull

On the universal constant in the Katz-Petrov and Osipov inequalities

Currently displaying 41 – 60 of 66