Related papers: On the asymptotics of drift
We consider a class of skew product maps of interval diffeomorphisms over the doubling map. The interval maps fix the end points of the interval. It is assumed that the system has zero fiber Lyapunov exponent at one endpoint and zero or…
We consider a nearest neighbor random walk on the one-dimensional integer lattice with drift towards the origin determined by an asymptotically vanishing function of the number of visits to zero. We show the existence of distinct regimes…
In this note we prove bounds on the upper and lower probability tails of sums of independent geometric or exponentially distributed random variables. We also prove negative results showing that our established tail bounds are asymptotically…
Although the theoretical behavior of one-dimensional random walks in random environments is well understood, the numerical evaluation of various characteristics of such processes has received relatively little attention. This paper develops…
Consider a random walk $S_n=\sum_{i=1}^n X_i$ with independent and identically distributed real-valued increments $X_i$ of zero mean and finite variance. Assume that $X_i$ is non-lattice and has a moment of order $2+\delta$. For any $x\geq…
Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the…
We study the asymptotic behavior of a nonlattice random walk in a general cone of $R^d$ . Following the approach initiated by D. Denisov and V. Wachtel in [8], we use a strong approximation of random walks by the Brownian motion and prove…
We count cycles of an unbounded length in generalized Johnson graphs. Asymptotics of the number of such cycles is obtained for certain growth rates of the cycle length.
We consider a variant of random walks on finite groups. At each step, we choose an element from a set of generators ("directions") uniformly, and an integer from a power law ("speed") distribution associated with the chosen direction. We…
We prove bounded rational ergodicity for some discrepancy skew products whose rotation number has bad rational approximation. This is done by considering the asymptotics of associated affine random walks.
We derive logarithmic asymptotics of probabilities of small deviations for iterated processes in the space of trajectories. We find conditions under which these asymptotics coincide with those of processes generating iterated processes.…
In the present paper we find necessary and sufficient conditions for recurrence of random walks on arbitrary subgroups of the group of rational numbers $\mathbb{Q}$.
A navigation on a set of points $S$ is a rule for choosing which point to move to from the present point in order to progress toward a specified target. We study some navigations in the plane where $S$ is a non uniform Poisson point process…
We examine asymptotic dimension and property A for groups acting on complexes. In particular, we prove that the fundamental group of a finite, developable complex of groups will have finite asymptotic dimension provided the geometric…
A statistic can be a function of multiple samples. There is little existing work on asymptotic theory for such statistics when group membership is random. We propose a flexible framework that can handle both deterministic and random…
We present a Darboux-Wiener type lemma and apply it to obtain an exact asymptotic for the variance of the self-intersection of one and two-dimensional random walks. As a corollary, we obtain a central limit theorem for random walk in random…
Critical catalytic branching random walk on d-dimensional integer lattice is investigated for all d. The branching may occur at the origin only and the start point is arbitrary. The asymptotic behavior, as time grows to infinity, is…
We exhibit a procedure to asymptotically enumerate monotone grid classes of permutations. This is then applied to compute the asymptotic number of permutations in any connected one-corner class. Our strategy consists of enumerating the…
We show that a random walk on the mapping class group of an orientable surface of finite type makes linear progress in the relative metric, which is quasi-isometric to the complex of curves.
Consider continuous-time random walks on Cayley graphs where the rate assigned to each edge depends only on the corresponding generator. We show that the limiting speed is monotone increasing in the rates for infinite Cayley graphs that…