Related papers: Loop measures without transition probabilities

Given a uniformly expanding transitive Markov interval map, we show that within the set of ergodic measures the set of nonadapted ergodic measures is residual in with respect to the topology induced by the $\overline{d}$-metric. This set of…

We prove a quantitative equidistribution result for linear random walks on the torus, similar to a theorem of Bourgain, Furman, Lindenstrauss and Mozes, but without any proximality assumption.

Conventional quantum mechanics describes a pre- and post-selected system in terms of virtual (Feynman) paths via which the final state can be reached. In the absence of probabilities, a weak measurement (WM) determines the probability…

We study the problem of mapping an unknown mixed quantum state onto a known pure state without the use of unitary transformations. This is achieved with the help of sequential measurements of two non-commuting observables only. We show that…

We investigate the asymptotic properties of permutations drawn from the Luce model, a natural probabilistic framework in which permutations are generated sequentially by sampling without replacement, with selection probabilities…

In the paper we study closures of classes of log--concave measures under taking weak limits, linear transformations and tensor products. We consider what uniform measures on convex bodies can one obtain starting from some class…

We construct examples of a random walk with pairwise-independent steps which is almost-surely bounded, and for any $m$ and $k$ a random walk with $k$-wise independent steps which has no stationary distribution modulo $m$.

We present some rigorous results on the absence of a wide class of invariant measures for dynamical systems possessing attractors. We then consider a generalization of the classical nonholonomic Suslov problem which shows how previous…

Concentration bounds for non-product, non-Haar measures are fairly recent: the first such result was obtained for contracting Markov chains by Marton in 1996 via the coupling method. The work that followed, with few exceptions, also used…

Let X and Y be independent transient Markov chains on the same state space that have the same transition probabilities. Let L denote the ``loop-erased path'' obtained from the path of X by erasing cycles when they are created. We prove that…

In this note we construct Markov partitions for non-transitive expansive flows in dimension 3.

We argue that the mean crossing number of a random polymer configuration is simply a measure of opacity, without being closely related to entanglement as claimed by several authors. We present an easy way of estimating its asymptotic…

A probability measure is a characteristic measure of a topological dynamical system if it is invariant to the automorphism group of the system. We show that zero entropy shifts always admit characteristic measures. We use similar techniques…

We establish convergence to an invariant measure as time tends to infinity, for a large class of (possibly non-Markovian) stochastic volatility models. Our arguments are based on a novel coupling idea for Markov chains which also extends to…

Quantum measurements are noncontextual, with outcomes independent of which other commuting observables are measured at the same time, when consistently analyzed using principles of Hilbert space quantum mechanics rather than classical…

We consider deconvolution from repeated observations with unknown error distribution. So far, this model has mostly been studied under the additional assumption that the errors are symmetric. We construct an estimator for the non-symmetric…

The infinite two-sided loop-erased random walk (LERW) is a measure on infinite self-avoiding walks that can be viewed as giving the law of the `middle part' of an infinite LERW loop going through 0 and infinity. In this note we derive…

Many of the conceptual problems students have in understanding quantum mechanics arise from the way probabilities are introduced in standard (textbook) quantum theory through the use of measurements. Introducing consistent microscopic…

Weak Feller property of controlled and control-free Markov chains lead to many desirable properties. In control-free setups this leads to the existence of invariant probability measures for compact spaces and applicability of numerical…

The trajectories of diffusion processes are continuous but non-differentiable, and each occurs with vanishing probability. This introduces a gap between theory, where path probabilities are used in many contexts, and experiment, where only…