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Iterative Schemes for Markov Perfect Equilibria
Felix H\"ofer, Mathieu Lauri\`ere, H. Mete Soner, Qinxin Yan
https://arxiv.org/abs/2507.20898 https://…

Iterative Schemes for Markov Perfect Equilibria
We study Markov perfect equilibria in continuous-time dynamic games with finitely many symmetric players. The corresponding Nash system reduces to the Nash-Lasry-Lions equation for the common value function, also known as the master equation in the mean-field setting. In the finite-state space problems we consider, this equation becomes a nonlinear ordinary differential equation admitting a unique classical solution. Leveraging this uniqueness, we prove the convergence of both Picard and weight…

On $q$-deformed Markov numbers. Cohn matrices and perfect matchings with weighted edges
Sam Evans, Perrine Jouteur, Sophie Morier-Genoud, Valentin Ovsienko
https://arxiv.org/abs/2507.19080

On $q$-deformed Markov numbers. Cohn matrices and perfect matchings with weighted edges
We consider a natural $q$-deformation of the classical Markov numbers. This $q$-deformation is closely related to $q$-deformed rational numbers recently introduced by two of us. Both notions, those of $q$-rationals and $q$-Markov numbers, are based on invariance with respect to the action of the modular group $mathrm{PSL}(2,\mathbb{Z})$. We prove that every Markov number has a unique $q$-deformation, which is a monic unimodal palindromic Laurent polynomial with positive integer coefficients. Th…

This https://arxiv.org/abs/2412.11313 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Stable Recovery of Regularized Linear Inverse Problems
Recovering a low-complexity signal from its noisy observations by regularization methods is a cornerstone of inverse problems and compressed sensing. Stable recovery ensures that the original signal can be approximated linearly by optimal solutions of the corresponding Morozov or Tikhonov regularized optimization problems. In this paper, we propose new characterizations for stable recovery in finite-dimensional spaces, uncovering the role of nonsmooth second-order information. These insights en…

A large hole in pseudo-random graphs
Sahar Diskin, Michael Krivelevich, Itay Markbreit, Maksim Zhukovskii
https://arxiv.org/abs/2505.23384 https://

A large hole in pseudo-random graphs
We show that there exist constants $δ_1,δ_2>0$ such that if $G$ is an $(n,d,λ)$-graph with $λ/d\leδ_1$, then $G$ contains an induced cycle of length at least $δ_2n/d$. We further demonstrate that, up to a constant factor, this is best possible. Utilising our techniques, we derive that the number of non-isomorphic induced subgraphs of such $G$ is at least exponential in $n\log d/d$, and further demonstrate that this is tight up to a constant factor in the exponent.

Trump in his Scottish enclave, spilling hatred against migrants and myths about wind power.
Trump habla de "invasión" de migrantes a Europa en su campo de golf de Escocia mientras emerge la idea del indulto a la mano derecha de Epstein

Trump habla de "invasión" de migrantes a Europa en su campo de golf de Escocia mientras emerge la idea del indulto a la mano derecha de Epstein
El presidente de EEUU muestra su irritación cuando se le pregunta por un caso del que no logra zafarse en vísperas de verse con el primer ministro británico, Keir Starmer, y la presidenta de la Comisión Europea, Ursula von der Leyen, en sus posesiones en Escocia

This https://arxiv.org/abs/2412.11313 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Stable Recovery of Regularized Linear Inverse Problems
Recovering a low-complexity signal from its noisy observations by regularization methods is a cornerstone of inverse problems and compressed sensing. Stable recovery ensures that the original signal can be approximated linearly by optimal solutions of the corresponding Morozov or Tikhonov regularized optimization problems. In this paper, we propose new characterizations for stable recovery in finite-dimensional spaces, uncovering the role of nonsmooth second-order information. These insights en…

Temperature dependence of quasi-localized phonons-mediated non-Markovianity dynamics of SiV^- centers in diamond
Wanggui Ye, Debao Zhang, Xuguang Cao, Ji Zhou, Xinye Fan, Sicheng Liu, Ke Yu, Jiqiang Ning, Shijie Xu
https://arxiv.org/abs/2506.19317

Temperature dependence of quasi-localized phonons-mediated non-Markovianity dynamics of SiV^- centers in diamond
Here we investigate the temperature-dependent non-Markovian dynamics of the SiV^- center in diamond, focusing on the roles of low- and high-frequency quasi-localized phonon modes. Low-frequency phonons exhibit stronger electron-phonon coupling, leading to long-lived dephasing rate, while high-frequency phonons induce rapid attenuation of oscillatory dephasing rate facilitating a persistent memory effect. The non-Markovianity measure N_C shows memory effects persisting at low temperatures but di…

Noise-tolerant tomography of multimode linear optical interferometers with single photons
Yu. A. Biriukov, R. D. Morozov, I. V. Dyakonov, M. V. Rakhlin, A. I. Galimov, G. V. Klimko, S. V. Sorokin, I. V. Sedova, M. M. Kulagina, Yu. M. Zadiranov, A. A. Toropov, A. A. Korneev, S. P. Kulik, S. S. Straupe
https://arxiv.org/abs/2506.2…

Noise-tolerant tomography of multimode linear optical interferometers with single photons
Linear optical networks are fundamental to the advancement of quantum technologies, including quantum computing, communication, and sensing. The accurate characterization of these networks, described by unitary matrices, is crucial to their effective utilization and scalability. In this work, we present the method for reconstructing the transfer matrix of a linear optical interferometer based on the analysis of cross-correlation functions of photon counts between pairs of output modes. Our appr…

Faster Fixed-Point Methods for Multichain MDPs
Matthew Zurek, Yudong Chen
https://arxiv.org/abs/2506.20910 https://arxiv.org/pdf/2506…

Faster Fixed-Point Methods for Multichain MDPs
We study value-iteration (VI) algorithms for solving general (a.k.a. multichain) Markov decision processes (MDPs) under the average-reward criterion, a fundamental but theoretically challenging setting. Beyond the difficulties inherent to all average-reward problems posed by the lack of contractivity and non-uniqueness of solutions to the Bellman operator, in the multichain setting an optimal policy must solve the navigation subproblem of steering towards the best connected component, in additi…

Long run control of nonhomogeneous Markov processes
{\L}ukasz Stettner
https://arxiv.org/abs/2506.15542 https://arxiv.org/pdf/2506.15…

Long run control of nonhomogeneous Markov processes
In the paper average reward per unit time and average risk sensitive reward functionals are considered for controlled nonhomogeneous Markov processes. Existence of solutions to suitable Bellman equations is shown. Continuity of the value functions with respect to risk parameter is also proved. Finally stability of functionals with respect to pointwise convergence of Markov controls is studied.