Related papers: Correspondence between noisy sample space reducing…

Motivated by recent experiments in neuroscience which indicate that neuronal avalanches exhibit scale invariant behavior similar to self-organized critical systems, we study the role of noisy (non-conservative) local dynamics on the…

In a continuous time random walk (CTRW), each random jump follows a random waiting time. CTRW scaling limits are time-changed processes that model anomalous diffusion. The outer process describes particle jumps, and the non-Markovian inner…

The following random recurrency: $$ W_{n+1} = U_{n+1} ( W_n + \Lambda_{n+1} ) $$ where $W_{-1}=0.$ is known to be associated with the shot noise : $$ W_{t} = \sum_{0<t_k<t} \Lambda_{k} e^{-(t-t_k)} $$ where the $t_k$ are the dates of a…

Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises"…

We study the sensitivity to noise of |permanent(X)|^2 for random real and complex n x n Gaussian matrices X, and show that asymptotically the correlation between the noisy and noiseless outcomes tends to zero when the noise level is…

Noisy labels are ubiquitous in real-world datasets, which poses a challenge for robustly training deep neural networks (DNNs) as DNNs usually have the high capacity to memorize the noisy labels. In this paper, we find that the test accuracy…

We show the asymptotic long-time equivalence of a generic power law waiting time distribution to the Mittag-Leffler waiting time distribution, characteristic for a time fractional CTRW. This asymptotic equivalence is effected by a…

This work explores a synchronization-like phenomenon induced by common noise for continuous-time Markov jump processes given by chemical reaction networks. A corresponding random dynamical system is formulated in a two-step procedure, at…

The random walk process in a nonhomogeneous medium, characterised by a L\'evy stable distribution of jump length, is discussed. The width depends on a position: either before the jump or after that. In the latter case, the density slope is…

Wavefunction collapse models modify Schr\"odinger's equation so that it describes the collapse of a superposition of macroscopically distinguishable states as a dynamical process. This provides a basis for the resolution of the quantum…

Reflecting boundary conditions cause two one-dimensional random walks to synchronize if a common direction is chosen in each step. The mean synchronization time and its standard deviation are calculated analytically. Both quantities are…

We present large deviations estimates in the supremum norm for a system of independent random walks superposed with a birth-and-death dynamics evolving on the discrete torus with $N$ sites. The scaling limit considered is the so-called…

Meta distribution is a fine-grained unified performance metric that enables us to evaluate the {reliability and latency} of next generation wireless networks, in addition to the conventional coverage probability. In this paper, using…

Survival analysis aims to estimate a time-to-event distribution from data with censored observations. Many existing methods either impose structural assumptions on the hazard function or discretize the time axis, which may limit flexibility…

We establish scaling limits for the random walk whose state space is the range of a simple random walk on the four-dimensional integer lattice. These concern the asymptotic behaviour of the graph distance from the origin and the spatial…

A key objective in spatial statistics is to simulate from the distribution of a spatial process at a selection of unobserved locations conditional on observations (i.e., a predictive distribution) to enable spatial prediction and…

We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process,…

We propose a variety of models of random walk, discrete in space and time, suitable for simulating stable random variables of arbitrary index $\alpha$ ($0< \alpha \le 2$), in the symmetric case. We show that by properly scaled transition to…

This paper studies a problem of Bayesian parameter estimation for a sequence of scaled counting processes whose weak limit is a Brownian motion with an unknown drift. The main result of the paper is that the limit of the posterior…

Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of…