New papers on Probability
176 new papers on probability in the last 7 days, within Math & statistics. These are the 50 Pipette rates most worth reading, with the main result in the authors' own words.
The best of the week
Distributed Stochastic Approximation Algorithms and Heavy-Tailed Age of Information
To the best of our knowledge, ours is the first analysis under general heavy-tailed AoI with potentially infinite mean.
PreprintClaims a big stepThe Most Informative Bit and Beyond: A Proof of the Courtade--Kumar Conjecture and Multibit Extensions
We prove the conjecture in every dimension and for every crossover probability, without a balance assumption.
PreprintClaims a big stepSpaceDiffusion: Over-the-Orbit Diffusion for Space Generate-and-Forward Communications
Experimental results demonstrate that SpaceDiffusion achieves lower end-to-end latency compared to DF scheme with retransmission protocol and saves approximately 15 dB of uplink transmit power at a target perceptual quality.
PreprintReal-world useFeedback Coding Enables Inference-Time Covert Agentic Communication
Based on this perspective, we introduce Burnashev Adaptive Posterior Matching (BAM), a feedback-coding scheme that combines posterior matching with a decode-and-confirm phase.
PreprintBold claims, read criticallyReal-world useSample-Based Prophet Inequalities for Random Walks
For the infinite-horizon setting, we establish a sharp prophet inequality with constant .
PreprintRepeated averaging on expanders I: random -regular graph
Specifically, we prove cutoff with a Gaussian profile on random -regular graphs, for any and uniformly over starting vertices.
PreprintEigenvalue and Eigenvector Approximation for Random Matrices Using Low-Degree Polynomials
For spiked GOE , we identify to be the critical degree threshold above which accurate approximation of the top eigenvalue and eigenvector is possible.
PreprintThe quasi-isometry classes of Galton--Watson trees
We classify, up to quasi-isometry, the large-scale geometry of Galton--Watson trees for every finitely supported offspring distribution.
PreprintCounterexamples to the Ramos conjecture for two hyperplanes
This disproves the Ramos conjecture for two hyperplanes.
PreprintConcentration of Regularized Sparse Random Matrices: Spectral Edge Bounds via Nonbacktracking Operators
For the first time in the literature, we provide variance- and cutoff-dependent bounds for extreme singular values and eigenvalues of regularized inhomogeneous random matrices.
PreprintInterference-Free Capacity of a Binary Interference Channel with Causal Observation
We determine the capacity region of a two-user binary interference channel with receiver-controlled observation and prove that causal port selection attains the interference-free limit.
PreprintStopping models closed under pgf composition, and the stability of randomly stopped model extensions
We characterize the complete set of stopping models for which randomly stopped sum and extreme model transformations function as statistically stable (idempotent) model extensions.
PreprintLocal Weak Limits for Equilibrium and Risk in Economic Networks
Under marked local weak convergence, we prove convergence in probability of the empirical equilibrium distribution in two settings: uniformly contractive responses and bounded monotone nonexpansive responses whose lower and upper root iterations coalesce.
PreprintDirected distances in spanning-tree-decorated planar maps: exact exponent, scaling limit and universality
We also show that in a uniform spanning-tree-decorated map with edges, directed distances are typically of order .
PreprintHigh-Dimensional Ultra-Log-Concave Distributions
In this paper, we introduce a quantitative high-dimensional extension of this notion, called -ultra-log-concavity, for probability measures on with downward closed support.
PreprintCompressible stochastic fluid--structure interaction with transport noise and Navier slip: A stochastic-flow approach
This paper establishes the existence of local martingale solutions for a three-dimensional stochastic fluid--structure interaction (FSI) problem coupling a viscous compressible isentropic fluid with an elastic shell through Navier-slip boundary conditions.
PreprintOn the Information-Theoretic Limits of Latent-Space Watermarking Through Pretrained Generators
For finite alphabets, we derive rate--key inner and outer bounds and characterize the coding and coordination requirements for realizing watermark communication through the prescribed latent interface.
PreprintOn Fast-Slow Mean-Field Forward-Backward Stochastic Systems
We establish an averaging principle for a class of multiscale mean-field forward-backward stochastic differential equations and identify several novel phenomena that are absent from classical fast-slow systems.
PreprintWell-posedness for Wright--Fisher SPDEs with measurable drift
We prove weak existence and uniqueness in law of -valued solutions for a class of scalar stochastic heat equations with measurable drifts , driven by Wright--Fisher noise.
PreprintNeSTR: Neural S-Transform Reconstruction for Gaussian SPDEs
The main novelty of NeSTR is an inverse -Transform reconstruction principle combined with finite mode learning: we prove consistency of the recovered chaos coefficients, separate noise mode, chaos truncation, deterministic solver, and neural approximation errors, and give a deterministic learning formulation for the restricted transform.
PreprintLong-time behavior of McKean--Vlasov stochastic systems with singular coefficients
We develop a quantitative framework for the long-time behavior of McKean--Vlasov stochastic differential equations with singular coefficients and possible phase transitions.
PreprintA Probabilistic Modeling Framework for Transient Debris Outcomes in Low Lunar Orbits
The framework develops continuous distributions for the probability of sinking (lunar collision) and non-sinking over these transient time horizons, building upon NASA's Standard Breakup Model to provide insights into the variations in the likelihood of debris outcomes across the LLO regime and offering an alternative to computationally expensive Monte Carlo simulations.
PreprintReal-world useDiscrete Isoperimetric Inequalities via Curvature
We develop a curvature-based semigroup framework to establish isoperimetric inequalities for measures with weakly dependent coordinates.
PreprintA Functional Central Limit Theorem for Locally Stationary Time Series in Banach Spaces
A functional central limit theorem for locally stationary time series taking values in a separable Banach space is established.
PreprintThe Sharp R\'enyi and Tsallis Threshold in the Shepp--Olkin Concavity Problem
We determine both thresholds exactly.
PreprintStochastic Domination of Gaussian Maxima by the Regular Simplex
We prove for every , and for each fixed equality holds only when for all .
PreprintCode availableThe Risk-Sensitive Schr\"odinger Bridge: Is Not a KL Projection
When the expected path cost is replaced by the entropic risk measure and both endpoint marginals are kept as hard constraints, the resulting fixed-point bridge value (the soft-problem value at the multiplier that enforces the terminal constraint) admits no representation as a constrained KL minimum against any fixed path-space reference with a regular endpoint law (a class strictly larger than the uniformly elliptic diffusion references: no Markov property is required), even allowing an additive normalisation depending on the initial marginal.
PreprintNoncommutative -integrators and stochastic differential equations in
We propose a new framework for noncommutative stochastic integration in , inspired by Bichteler's notion of -integrators, that massively generalizes our previous theory of -valued stochastic integration against -decomposable processes.
PreprintFinite-state counterexamples to Ross's second queueing conjecture
We construct finite-state Markov arrival-rate processes for which faster modulation increases the mean stationary workload of a stable single-server queue, disproving the universal ordering in Leskel\"a's formulation of Ross's second conjecture.
PreprintTrefoil Probabilities and Polyhedra
We determine the exact probability that the closed hexagonal polygon obtained by cyclically joining six independent points uniformly distributed on the unit sphere is knotted.
PreprintRecurrence and transience of random walks on monotonically changing environments
We prove that if and is recurrent (respectively, is transient), then is almost surely recurrent (respectively, transient), i.e., visits every vertex infinitely (respectively, finitely) often.
PreprintGaussian Vertex-Face Balance in Random Convex Polyhedra with Fixed Edge Count
This resolves a fixed-edge limit-distribution question posed by R\"udinger: if , then , equivalently .
PreprintShrinking-Tube Concentration for Adaptive Markovian Stochastic Approximation
We establish a shrinking-tube concentration bound for projected stochastic approximation driven by an adaptive Markov chain.
PreprintOne-Shot Information Hiding and Compound Wiretap Channels
We derive novel one-shot achievability results for both problems that are applicable to any source distribution and any class of channels (not necessarily memoryless or ergodic), and that apply to both discrete and continuous cases.
PreprintRemote IoT Source Monitoring with Delayed Feedback
Our study characterizes the fundamental trade-off between estimation error and communication rate, revealing that proactive transmissions significantly improve MSE even under strict IoT rate constraints.
PreprintMarkovization of Randomized Stopping Times
We prove that every admissible intensity has a Markovian representative , explicitly obtained from the observed measure and the surviving occupation measure.
PreprintTotal Variation Distance between Product Distributions: an Analytic Proxy
We characterize, up to universal constants, the total variation distance between finite products of arbitrary probability measures by a simple formula.
PreprintInfinite-dimensional Dyson Brownian motion(s)
We study infinite-dimensional Dyson Brownian motions obtained as limits of finite systems without rescaling the actual stochastic dynamics.
PreprintQuantitative QSD convergence in 1-Wasserstein distance via the F\"ollmer drift
Under a general ergodicity condition on the associated Feynman-Kac semigroup, we then establish the existence of a QSD with a large domain of attraction, and the exponentially fast convergence to it of the conditioned semigroup in the -Wasserstein distance as goes to infinity.
PreprintRisk diversification for infinitely divisible distributions
We characterize, in terms of subadditivity and concavity of the transformed L\'{e}vy measures, L\'{e}vy processes that exhibit the non-diversification phenomenon or the reverse diversification order with respect to the majorization order uniformly over all time horizons.
PreprintVillani's conjecture for Kac's walk
We prove Villani's conjecture on entropy production for Kac's walk with uniform collision angles.
PreprintCapacity of a Mixed Multiple-Access Channel with Causal Observation
We determine the capacity region of a mixed binary multiple-access channel whose receiver can choose how each observation is formed.
PreprintThe joint exit time and exit location law of a planar Ornstein-Uhlenbeck process on annular sectors and principal axis rectangles
In this way we obtain the survival probability, the density and moments of the exit time, and -the principal contribution -the joint law of the exit time and the exit boundary, which resolves both the instant of exit and the boundary piece through which it occurs.
PreprintBlock Erasure Channel and Block z-Channel with Bounded Decoders and Finite Blocklength
We derive a rigorous upper bound and a companion lower-side estimate on the block confusion probability (BLCP) and block erasure probability (BLEP) for bounded-distance decoders over additive white Gaussian noise (AWGN) channels at finite blocklength, recasting the coding problem as a geometric sphere packing one.
PreprintGeometry and observability of latent texture-coherence diffusions in coherent sea-clutter radar observations
For fixed-shape fast covariance, we derive an exact generalized spectral-gap criterion for recovery of the latent slow coordinate and a stability bound.
PreprintSharp High-Entropy Bounds for Sums of Independent Discrete Random Variables
We prove that independent discrete random variables with finite Shannon entropies satisfy in every torsion-free abelian group as .
PreprintSensing Assisted Satellite Backhaul with FBL UL and Broadcast DL for Massive IoT
In this paper, we pro- pose a unified end-to-end framework for satellite-assisted massive IoT networks that jointly models uplink FBL random access, sensing assisted satellite backhaul, and worst user broadcast downlink transmission.
Preprint with a published versionReal-world useA Deep BSDE Method for a Class of Strongly Coupled FBSDEs
The key novelty is that we establish an a-posteriori convergence result for the approximation of strongly coupled forward-backward stochastic differential equations (FBSDEs), i.e., our result holds without any assumptions on small time horizons, monotonicity or weak coupling that are typically imposed in the literature on the deep BSDE method.
PreprintQuantitative propagation of chaos in total variation for unregularized Vlasov--Riesz--Fokker--Planck systems
We establish quantitative propagation of chaos in total variation for the unregularized three-dimensional repulsive Vlasov--Poisson--Fokker--Planck (VPFP) particle system.
PreprintOptimal support and condensation in random allocations
For , the profile records the reduction in the logarithm of the number of compatible words caused by repetitions; we show that once the normalized profile exceeds , the limiting optimal fraction is pinned at .
Preprint