Related papers: An introduction to higher walks
We have formulated higher-order integration by parts formulae on the path space restricted between two curves, with respect to pinned/ordinary Wiener measures. The higher-order integration by parts formulae introduce nontrivial boundary…
Expander graphs are among the most useful combinatorial objects in theoretical computer science. A line of work studies random walks on expander graphs for their pseudorandomness against various classes of test functions, including…
A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…
Higher-order interactions have recently emerged as a promising framework for describing new dynamical phenomena in heterogeneous contagion processes. However, a fundamental open question is how to understand their contribution from the…
A treap is a classic randomized binary search tree data structure that is easy to implement and supports O(\log n) expected time access. However, classic treaps do not take advantage of the input distribution or patterns in the input. Given…
Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time…
In dealing with thermal transport in composite systems, high contrast materials pose a special problem for numerical simulation: the time scale or step size in the high conductivity material must be much smaller than in the low conductivity…
A rotor-router walk is a deterministic version of a random walk, in which the walker is routed to each of the neighbouring vertices in some fixed cyclic order. We consider here directed covers of graphs (called also periodic trees) and we…
One approach to study the pseudorandomness properties of walks on expander graphs is to label the vertices of an expander with elements from an alphabet $\Sigma$, and study the mean of functions over $\Sigma^n$. We say expander walks…
We study high order random walks in high dimensional expanders; namely, in complexes which are local spectral expanders. Recent works have studied the spectrum of high order walks and deduced fast mixing. However, the spectral gap of high…
Random walks describe diffusion processes, where movement at every time step is restricted to only the neighbouring locations. We construct a quantum random walk algorithm, based on discretisation of the Dirac evolution operator inspired by…
The starting point is the known fact that some much-studied random walks on permutations, such as the Tsetlin library, arise from walks on real hyperplane arrangements. This paper explores similar walks on complex hyperplane arrangements.…
Many recent papers deal with the enumeration of 2-dimensional walks with prescribed steps confined to the positive quadrant. The classification is now complete for walks with steps in $\{0, \pm 1\}^2$: the generating function is D-finite if…
In this article, we consider several models of random walks in one or several dimensions, additionally allowing, at any unit of time, a reset (or "catastrophe") of the walk with probability $q$. We establish the distribution of the final…
We propose a new family of discrete-spacetime quantum walks capable to propagate on any arbitrary triangulations. Moreover we also extend and generalize the duality principle introduced by one of the authors, linking continuous local…
We consider the precise upper large deviations estimates for the maximal displacement of a branching random walk. In addition, we obtain a description of the extremal process of the branching random walk conditioned on this large deviations…
This paper investigates the geometric structure of higher-derivative formulations of classical mechanics. It is shown that every even-order formulation of classical mechanics higher than the second order is intrinsically variational, in the…
The aim of this work is to further develop the calculus of (internal) relations for a regular Ord-category C. To capture the enriched features of a regular Ord-category and obtain a good calculus, the relations we work with are precisely…
The main theme of this dissertation is retooling methods to work for different situations. I have taken the method derived by O'Hara and simplified by Zeilberger to prove unimodality of $q$-binomials and tweaked it. This allows us to create…
We introduce an extension of Hoare logic for call-by-value higher-order functions with ML-like local reference generation. Local references may be generated dynamically and exported outside their scope, may store higher-order functions and…