Related papers: Point processes and stochastic displacement fields

Deep learning algorithms have made incredible strides in the past decade, yet due to their complexity, the science of deep learning remains in its early stages. Being an experimentally driven field, it is natural to seek a theory of deep…

In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…

Stochastic processes on topological vector spaces over non-Archimedean fields and with transition measures having values in non-Archimedean fields are defined and investigated. For this the non-Archimedean analog of the Kolmogorov theorem…

In recent years, there has been considerable interest in understanding the motion in Hamiltonian systems when phase space is divided into stochastic and integrable regions. This paper studies one aspect of this problem, namely, the motion…

A problem of practical significance is the analysis of large, spatially distributed data sets. The problem is more challenging for variables that follow non-Gaussian distributions. We show that the spatial correlations between variables can…

We present a comprehensive study of the phase transitions in the single-field reaction-diffusion stochastic systems with field-dependent mobility of a power-low form and the internal fluctuations. Using variational principles and mean-field…

The two-species symbiotic contact process (2SCP) is a stochastic process where each vertex of a graph may be vacant or host at most one individual of each species. Vertices with both species have a reduced death rate, representing a…

A stochastic process, when subject to resetting to its initial condition at a constant rate, generically reaches a non-equilibrium steady state. We study analytically how the steady state is approached in time and find an unusual relaxation…

Stochastic processes on totally disconnected topological groups are investigated. In particular they are considered for diffeomorphism groups and loop groups of manifolds on non-Archimedean Banach spaces. Theorems about a quasi-invariance…

This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…

Quantifying how distinguishable two stochastic processes are lies at the heart of many fields, such as machine learning and quantitative finance. While several measures have been proposed for this task, none have universal applicability and…

We consider two different collective spin systems subjected to strong dissipation -- on the same scale as interaction strengths and external fields -- and show that either continuous or discontinuous dissipative quantum phase transitions…

Of stochastic differential equations, diffusion processes have been adopted in numerous applications, as more relevant and flexible models. This paper studies diffusion processes in a different setting, where for a given stationary…

We derive exact analytic results for several four-point correlation functions for statistical models exhibiting phase separation in two-dimensions. Our theoretical results are then specialized to the Ising model on the two-dimensional strip…

Dispersal between different habitats influences the dynamics and stability of populations considerably. Furthermore, these effects depend on the local interactions of a population with other species. Here, we perform a general and…

The article is devoted to stochastic processes with values in finite-dimensional vector spaces over infinite locally compact fields with non-trivial non-archimedean valuations. Infinitely divisible distributions are investigated. Theorems…

We introduce a family of local inhomogeneous mark-weighted summary statistics, of order two and higher, for general marked point processes. Depending on how the involved weight function is specified, these summary statistics capture…

A one dimensional exclusion process is introduced where particles hop to a neighbouring vacant site with a rate that depends on the size of the block they belong to. This model is equivalent to a zero range process (ZRP) and shares the same…

Stochastic processes are considered on free loop spaces, geometric loop and diffeomorphism groups of real and complex manifolds. They are used for investigations of Wiener differentiable quasi-invariant measures on such groups relative to…

Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…