A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study diffusions and random walks on hyperbolic spaces, focusing on their Martin boundaries.
Geodesic walks converge to Brownian motion on Finsler manifolds.
ParPIC clusters directed graphs using random walks and diffusion operators.
In network embedding, random walks play a fundamental role in preserving network structures. However, random walk based embedding methods have two limitations. First, random walk methods are fragile when the sampling frequency or the number of node sequences changes. Second, in disequilibrium networks such as highly bi…
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a diffusion equation with a diffusion coefficient that inversely depends on the dat…
DM uses semigroup property to tune diffusion time for better data analysis.
Graphs with bounded degrees and non-negative Ollivier-Ricci curvature have subexponential growth and diffusive random walk.
A new method improves graph random features with quasi-Monte Carlo techniques.
Study uniform convergence of random walk Laplacians to diffusion Laplacian on smooth manifolds.
For covering spaces and properly discontinuous actions with compatible diffusion processes, we discuss Lyons-Sullivan discretizations of the processes and the associated function theory.
NodeSig efficiently computes binary node embeddings for scalable graph analysis.
New algorithm uniformly samples high-dimensional convex bodies efficiently.
Neumann eigenmaps improve landmark-based diffusion map embeddings.
As a model of market price, we introduce a new type of random walk in a moving potential which is approximated by a quadratic function with its center given by the moving average of its own trace. The properties of resulting random walks are similar to those of ordinary random walks for large time scales; however, thei…
Graphs approximate semigroups for diffusion on Riemannian manifolds.
Unified framework for multi-view diffusion geometries using intertwined diffusion trajectories.
Simulates financial market orders using anomalous diffusion models.
We relate some basic constructions of stochastic analysis to differential geometry, via random walk approximations. We consider walks on both Riemannian and sub-Riemannian manifolds in which the steps consist of travel along either geodesics or integral curves associated to orthonormal frames, and we give particular at…
Study provides convergence guarantees for discrete diffusion models on finite and infinite state spaces.
A novel unified Bayesian framework for network detection is developed, under which a detection algorithm is derived based on random walks on graphs. The algorithm detects threat networks using partial observations of their activity, and is proved to be optimum in the Neyman-Pearson sense. The algorithm is defined by a …
Innovative extensions to option pricing models using asymmetric Brownian motion and random walk approaches.
EntroPath learns manifold geometry from diffusion paths.
Based on the new type of random walk process called the Potentials of Unbalanced Complex Kinetics (PUCK) model, we theoretically show that the price diffusion in large scales is amplified 2/(2 + b) times, where b is the coefficient of quadratic term of the potential. In short time scales the price diffusion depends on …
Several models of stock trading [P. Bak et al, Physica A {\bf 246}, 430 (1997)] are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the short-time market price variation is subdiffusive with a Hurst exponent . Biase…
An unsupervised learning algorithm to cluster hyperspectral image (HSI) data is proposed that exploits spatially-regularized random walks. Markov diffusions are defined on the space of HSI spectra with transitions constrained to near spatial neighbors. The explicit incorporation of spatial regularity into the diffusion…
Spectral clustering is widely used to partition graphs into distinct modules or communities. Existing methods for spectral clustering use the eigenvalues and eigenvectors of the graph Laplacian, an operator that is closely associated with random walks on graphs. We propose a new spectral partitioning method that exploi…
Continuous time random walks (CTRWs) are used in physics to model anomalous diffusion, by incorporating a random waiting time between particle jumps. In finance, the particle jumps are log-returns and the waiting times measure delay between transactions. These two random variables (log-return and waiting time) are typi…
We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this benchmark model is unable to reproduce the diffusion properties of real prices.…
We introduce a novel harmonic analysis for functions defined on the vertices of a strongly connected directed graph of which the random walk operator is the cornerstone. As a first step, we consider the set of eigenvectors of the random walk operator as a non-orthogonal Fourier-type basis for functions over directed gr…
A coupling by reflection of a time-inhomogeneous diffusion process on a manifold are studied. The condition we assume is a natural time-inhomogeneous extension of lower Ricci curvature bounds. In particular, it includes the case of backward Ricci flow. As in time-homogeneous cases, our coupling provides a gradient esti…
The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications in physics, but also in insurance, finance and economics. A definition is given for a class of stochastic integrals driven by a CTRW, that includes the Ito and Stratonovich cases. An uncoupled CTRW with zero-mean jumps is…
Model place cells as spatial embeddings for efficient path planning and cognitive map construction.
Study large deviations in random walks on Lie groups.
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…
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…
Quantum walks blend patterns into splines when averaged.
Local limit theorem for random walks on hyperbolic groups with parabolic subgroups.
Random walks on cell complexes link to Laplacians and Novikov-Shubin invariants.
Random walks on metric spaces embed quasi-isometrically into the space.
This work estimates edge weights of edge-reinforced random walks using observed data.
New proof shows rapid mixing for random walks on nilmanifolds.
Random walks on hyperbolic spaces show linear growth in translation lengths.
Study random walks on groups with superlinear divergent geodesics.
Study random walks on sub-Riemannian manifolds using retractions.
Finding the reduced-dimensional structure is critical to understanding complex networks. Existing approaches such as spectral clustering are applicable only when the full network is explicitly observed. In this paper, we focus on the online factorization and partition of implicit large-scale networks based on observati…
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.