Tootfinder

Reversible Imprecise Markov Chains
Damjan \v{S}kulj
https://arxiv.org/abs/2507.06374 https://arxiv.org/pdf/2507.06374

Reversible Imprecise Markov Chains
Reversible Markov chains have identical forward and backward path distributions; this symmetry yields tractable stationary behaviour and powers algorithms from MCMC to network random-walk analysis. We extend reversibility to imprecise Markov chains, in which marginal and transition probabilities are specified by credal sets. Adopting the strong-independence interpretation of the Markov property, we reverse every precise chain compatible with a given credal specification and study the resulting …

This https://arxiv.org/abs/2312.17387 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Algebraic dynamical systems from LDPC codes satisfy a strong negation of the weak Pinsker property
We construct an explicit algebraic example of a subshift of finite type over a group $Γ$ with an invariant Markov measure which has completely positive sofic entropy (with respect to `most' sofic approximations) and yet does not have a direct Bernoulli factor, because its model spaces shatter into exponentially many clusters of sub-exponential size. The example and its analysis are related to random low-density parity-check (LDPC) codes.

Markovian multivariate Hawkes population processes: Efficient evaluation of moments
R. S. Karim, R. J. A. Laeven, M, M. Mandjes
https://arxiv.org/abs/2506.08775

Markovian multivariate Hawkes population processes: Efficient evaluation of moments
We provide probabilistic and computational results on Markovian multivariate Hawkes processes and induced population processes. By applying the Markov property, we characterize in closed form a joint transform, bijective to the probability distribution, of the population process and its underlying intensity process. We demonstrate a method that exploits the transform to obtain analytic expressions for transient and stationary multivariate moments of any order, as well as auto- and cross-covaria…

Gaussian Invariant Markov Chain Monte Carlo
Michalis K. Titsias, Angelos Alexopoulos, Siran Liu, Petros Dellaportas
https://arxiv.org/abs/2506.21511 https:…

Gaussian Invariant Markov Chain Monte Carlo
We develop sampling methods, which consist of Gaussian invariant versions of random walk Metropolis (RWM), Metropolis adjusted Langevin algorithm (MALA) and second order Hessian or Manifold MALA. Unlike standard RWM and MALA we show that Gaussian invariant sampling can lead to ergodic estimators with improved statistical efficiency. This is due to a remarkable property of Gaussian invariance that allows us to obtain exact analytical solutions to the Poisson equation for Gaussian targets. These …

Transformers Beyond Order: A Chaos-Markov-Gaussian Framework for Short-Term Sentiment Forecasting of Any Financial OHLC timeseries Data
Arif Pathan
https://arxiv.org/abs/2506.17244

Transformers Beyond Order: A Chaos-Markov-Gaussian Framework for Short-Term Sentiment Forecasting of Any Financial OHLC timeseries Data
Short-term sentiment forecasting in financial markets (e.g., stocks, indices) is challenging due to volatility, non-linearity, and noise in OHLC (Open, High, Low, Close) data. This paper introduces a novel CMG (Chaos-Markov-Gaussian) framework that integrates chaos theory, Markov property, and Gaussian processes to improve prediction accuracy. Chaos theory captures nonlinear dynamics; the Markov chain models regime shifts; Gaussian processes add probabilistic reasoning. We enhance the framework…

This https://arxiv.org/abs/2205.07214 has been replaced.
link: https://scholar.google.com/scholar?q=a

Entropy Production for Discrete-Time Markov Processes
We study the multiple definitions of the entropy production for discrete-time Markov processes in single systems and composite systems. These definitions have been studied in single systems, but less so in composite systems. With a clear distinction, we review the equivalence condition and the meaning of the multiple definitions and show that all definitions satisfy the important property for the entropy production, such as non-negativity. We also show that the inequalities between total entrop…

This https://arxiv.org/abs/2505.16093 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Multiple chordal SLE($κ$) and quantum Calogero-Moser system
We study multiple chordal SLE$(κ)$ systems in a simply connected domain $Ω$, where $z_1, \ldots, z_n \in \partial Ω$ are boundary starting points and $q \in \partial Ω$ is an additional marked boundary point. As a consequence of the domain Markov property and conformal invariance, we show that the presence of the marked boundary point $q$ gives rise to a natural equivalence relation on partition functions. While these functions are not necessarily conformally covariant, each equivalence c…

Sampling and Identity-Testing Without Approximate Tensorization of Entropy
William Gay, William He, Nicholas Kocurek, Ryan O'Donnell
https://arxiv.org/abs/2506.23456

Sampling and Identity-Testing Without Approximate Tensorization of Entropy
Certain tasks in high-dimensional statistics become easier when the underlying distribution satisfies a local-to-global property called approximate tensorization of entropy (ATE). For example, the Glauber dynamics Markov chain of an ATE distribution mixes fast and can produce approximate samples in a small amount of time, since such a distribution satisfies a modified log-Sobolev inequality. Moreover, identity-testing for an ATE distribution requires few samples if the tester is given coordinat…

The Markov property for $\varphi^4_3$ on the cylinder
Nikolay Barashkov, Trishen S. Gunaratnam
https://arxiv.org/abs/2506.21466 https://

The Markov property for $φ^4_3$ on the cylinder
We prove that the $φ^4_3$ model satisfies a version of Segal's axioms in the special case of three-dimensional tori and cylinders. As a consequence, we give the first proof that this model satisfies a Markov property and we characterize its boundary law up to absolutely continuous perturbations. In addition, we use Segal's axioms to give an alternative construction of the $φ^4_3$ Hamiltonian on two-dimensional tori as compared with Glimm (Comm. Math. Phys., 1968). We exploit this probabilisti…

An infinite horizon sufficient stochastic maximum principle for regime switching diffusions and applications
Kai Ding, Xun Li, Siyu Lv, Xin Zhang
https://arxiv.org/abs/2506.11523 …

An infinite horizon sufficient stochastic maximum principle for regime switching diffusions and applications
This paper is concerned with a discounted stochastic optimal control problem for regime switching diffusion in an infinite horizon. First, as a preliminary with particular interests in its own right, the global well-posedness of infinite horizon forward and backward stochastic differential equations with Markov chains and the asymptotic property of their solutions when time goes to infinity are obtained. Then, a sufficient stochastic maximum principle for optimal controls is established via a d…

Stability conditions of chemical networks in a linear framework
Armand Despons, J\'er\'emie Unterberger, David Lacoste
https://arxiv.org/abs/2507.14941

Stability conditions of chemical networks in a linear framework
Autocatalytic chemical reaction networks can collectively replicate or maintain their constituents despite degradation reactions only above a certain threshold, which we refer to as the decay threshold. When the chemical network has a Jacobian matrix with the Metzler property, we leverage analytical methods developed for Markov processes to show that the decay threshold can be calculated by solving a linear problem, instead of the standard eigenvalue problem. We explore how this decay threshold…

Local-global correlations of dynamics on disordered energy landscapes
Jacob Calvert, Dana Randall
https://arxiv.org/abs/2508.04501 https://arxiv.org/pdf/25…

Local-global correlations of dynamics on disordered energy landscapes
The stationary distribution of a continuous-time Markov chain generally arises from a complicated global balance of probability fluxes. Nevertheless, empirical evidence shows that the effective potential, defined as the negative logarithm of the stationary distribution, is often highly correlated with a simple local property of a state: the logarithm of its exit rate. To better understand why and how typically this correlation is high, we study reversible reaction kinetics on energy landscapes …

On the validity of the Radon-Nikodym Theorem
Paolo Roselli, Michel Willem
https://arxiv.org/abs/2506.12023 https://arxiv.org/pdf/2506…

On the validity of the Radon-Nikodym Theorem
This paper presents a new general formulation of the Radon-Nikodym theorem in the setting of abstract measure theory. We introduce the notion of weak localizability for a measure and show that this property is both necessary and sufficient for the validity of a Radon-Nikodym-type representation under a natural compatibility relation between measures. The proof relies solely on elementary tools, such as Markov's inequality and the monotone convergence theorem. In addition to establishing the mai…

The intertwining property for $\beta $-Laguerre processes and integral operators for Jack polynomials
Yosuke Kawamato, Genki Shibukawa
https://arxiv.org/abs/2505.23139

The intertwining property for $β$-Laguerre processes and integral operators for Jack polynomials
The aim of this paper is to study intertwining relations for Laguerre process with inverse temperature $β\ge 1$ and parameter $α>-1$. We introduce a Markov kernel that depends on both $β$ and $ α$, and establish new intertwining relations for the $β$-Laguerre processes using this kernel. A key observation is that Jack symmetric polynomials are eigenfunctions of our Markov kernel, which allows us to apply a method established by Ramanan and Shkolnikov. Additionally, as a by-product, we deri…

This https://arxiv.org/abs/2505.14762 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Multiple radial SLE($κ$) and quantum Calogero-Sutherland system
In this first of two articles, we study the multiple radial $\mathrm{SLE}(κ)$ systems with parameter $κ> 0$ -- a family of random multi-curve systems in a simply-connected domain $Ω$, with marked boundary points $z_1, \ldots, z_n \in \partial Ω$ and a marked interior point $q$. As a consequence of the domain Markov property and conformal invariance, we show that such systems are characterized by equivalence classes of partition functions, which are not necessarily conformally covariant. Nev…