arXiv research

Several known results, by Rivin, Calegari-Maher and Sisto, show that an element $φ_n\in Out(F_r)$, obtained after $n$ steps of a simple random walk on $Out(F_r)$, is fully irreducible with probability tending to 1 as $n\to\infty$. In this paper we construct a natural "train-track directed" random walk $\mathcal W$ on $…

We prove a sharp estimate on the expected value of the integral of the index of a simple random walk on the square or triangular lattice. This gives new lower bounds on the averaged Dehn function, which measures the expected area needed to fill a random curve with a disc.

Graphs can model interactions between vertices, but how well depends on graph structure.

XGBoost predicts NEPSE Index log returns with low error and high directional accuracy.

Data-driven methods link graphon limits to random walks and spectral clustering.

It is known that every infinite index quasi-convex subgroup $H$ of a non-elementary hyperbolic group $G$ is a free factor in a larger quasi-convex subgroup of $G$. We give a probabilistic generalization of this result. That is, we show that when $R$ is a subgroup generated by independent random walks in $G$, then $\lan…

Gittins index optimizes decision-making under uncertainty, even in complex scenarios.

In this article, the long-term behavior of the stock market index of the New York Stock Exchange is studied, for the period 1950 to 2013. Specifically, the CRSP Value-Weighted and CRSP Equal-Weighted index are analyzed in terms of market efficiency, using the standard ratio variance test, considering over 1600 one week…

We consider the occurrence of record-breaking events in random walks with asymmetric jump distributions. The statistics of records in symmetric random walks was previously analyzed by Majumdar and Ziff and is well understood. Unlike the case of symmetric jump distributions, in the asymmetric case the statistics of reco…

We investigate the statistics of records in a random sequence $\{x_B(0)=0,x_B(1),\cdots, x_B(n)=x_B(0)=0\}$ of $n$ time steps. The sequence $x_B(k)$'s represents the position at step $k$ of a random walk `bridge' of $n$ steps that starts and ends at the origin. At each step, the increment of the position is a random ju…

We study the volatility of the MIB30-stock-index high-frequency data from November 28, 1994 through September 15, 1995. Our aim is to empirically characterize the volatility random walk in the framework of continuous-time finance. To this end, we compute the index volatility by means of the log-return standard deviatio…

Quantum stochastic walks optimize portfolios by leveraging financial networks, improving Sharpe ratios and reducing turnover.

Randomized control methods improve asset pricing and performance analysis.

We construct a new type of quantum walks on simplicial complexes as a natural extension of the well-known Szegedy walk on graphs. One can numerically observe that our proposing quantum walks possess linear spreading and localization as in the case of the Grover walk on lattices. Moreover, our numerical simulation sugge…

We propose a random walk model of asset returns where the parameters depend on market stress. Stress is measured by, e.g., the value of an implied volatility index. We show that model parameters including standard deviations and correlations can be estimated robustly and that all distributions are approximately normal.…

The paper tackles attributing forecast gaps in complex model suites.

This paper presents VEC-NBT, a variation on the unsupervised graph clustering technique VEC, which improves upon the performance of the original algorithm significantly for sparse graphs. VEC employs a novel application of the state-of-the-art word2vec model to embed a graph in Euclidean space via random walks on the n…

We propose and analyze two new MCMC sampling algorithms, the Vaidya walk and the John walk, for generating samples from the uniform distribution over a polytope. Both random walks are sampling algorithms derived from interior point methods. The former is based on volumetric-logarithmic barrier introduced by Vaidya wher…

Study large deviations in random walks on Lie groups.

The paper introduces walks with jumps for modeling neuron activity in hyperbolic space.

Quantum walks blend patterns into splines when averaged.

Unified view on random walk and Weisfeiler-Leman kernels, improving accuracy.

Local limit theorem for random walks on hyperbolic groups with parabolic subgroups.

We review recent advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a Lévy flight on a line. After a brief survey of the theory of records for independent and identically distributed random variables, we focus on random walks. During the last few…

Study random walks on sub-Riemannian manifolds using retractions.

Random walks on cell complexes link to Laplacians and Novikov-Shubin invariants.

Study diffusions and random walks on hyperbolic spaces, focusing on their Martin boundaries.

New proof shows rapid mixing for random walks on nilmanifolds.

Develops a binary tree model for option pricing with skew dynamics.

The paper finds braid representatives minimizing simple walks for knots.

Quantum walks model financial returns with flexibility and asymmetry.

Random walks on metric spaces embed quasi-isometrically into the space.

Study random walks on groups with superlinear divergent geodesics.

New walk extraction strategies improve node embeddings in KGs.

Random walks on hyperbolic spaces show linear growth in translation lengths.

Geodesic walks converge to Brownian motion on Finsler manifolds.

Market economy closely connects aspects to all walks of life. The stock forecast is one of task among studies on the market economy. However, information on markets economy contains a lot of noise and uncertainties, which lead economy forecasting to become a challenging task. Ensemble learning and deep learning are the…

The paper examines random walks on metric spaces and finds commensurable subgroups.

Random walks on free groups reveal asymmetric expansion factors.

Survey on random walks on mapping class groups and their properties.

This work estimates edge weights of edge-reinforced random walks using observed data.

Deviation inequalities and limit laws for random walks on metric spaces.

Random walks on Fuchsian Schottky groups have harmonic measures with lower dimension.

UniNet efficiently learns network representations from large graphs.

We study the statistics of the number of records R_{n,N} for N identical and independent symmetric discrete-time random walks of n steps in one dimension, all starting at the origin at step 0. At each time step, each walker jumps by a random length drawn independently from a symmetric and continuous distribution. We co…

We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly-decaying autocorrelation functions. The relation between these correlated walks and the well-kno…

We introduce the geodesic walk for sampling Riemannian manifolds and apply it to the problem of generating uniform random points from polytopes in R^n specified by m inequalities. The walk is a discrete-time simulation of a stochastic differential equation (SDE) on the Riemannian manifold equipped with the metric induc…

Uniform drift estimates found for random walks on graph products.