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Structural properties of the implicit function defined by an integral self-consistency equation

arXiv:2606.04243v1 Announce Type: new Abstract: We study the integral equation $\int_0^m \eta\rho(\eta)/(C-\eta)\,d\eta = 1$ with $C>m$, where $\rho$ is a $C^1$ probability density on $[0,M]$ vanishing polynomially at $\eta=M$. Setting $\mathcal{I}^+(m) := \lim_{C \downarrow m}\int_0^m \eta\rho(\eta)/(C-\eta)\,d\eta$ and $\Omega := \{m \in (0,M) : \mathcal{I}^+(m) > 1\}$, the equation determines $C$ implicitly as a function of $m$ on $\Omega$, and our object of study is the dimensionless...

arXiv CS 6d ago

A remark on the majorizing measures theorem for general processes

Announce Type: replace-cross Abstract: We show that the lower bound in the majorizing measures theorem holds for a large class of random vectors. Specifically, suppose $X \sim \mu$ is a centered random vector in $\mathbf{R}^n$ with \[ C_{\mathrm{KL}}(\mu) = \sup_{\substack{\theta \neq \eta \\ \theta, \eta \in \mathbf{R}^n}} \frac{\mathrm{KL}(\mu_\theta \| \mu_\eta)}{\|\theta - \eta\|_2^2} <

arXiv CS 6d ago

A remark on the majorizing measures theorem for general processes

arXiv:2606.03973v1 Announce Type: cross Abstract: We show that the lower bound in the majorizing measures theorem holds for a large class of random vectors. Specifically, suppose $X \sim \mu$ is a centered random vector in $\mathbf{R}^n$ with \[ C_{\mathrm{KL}}(\mu) = \sup_{\substack{\theta \neq \eta \\ \theta, \eta \in \mathbf{R}^n}} \frac{\mathrm{KL}(\mu_\theta \| \mu_\eta)}{\|\theta - \eta\|_2^2} <

arXiv CS 7d ago

The Privacy Subsidy in Glosten-Milgrom: Bid-Ask Spread and Welfare under Flip-Noise Direction Observation

arXiv:2605.19742v4 Announce Type: replace Abstract: We derive a closed-form bid-ask spread and welfare decomposition for the Glosten-Milgrom 1985 sequential-trading model when the market maker observes the trade direction perturbed by a binary flip channel of probability $\eta$ -- a natural information-theoretic model of privacy mechanisms acting on the direction signal. Under a committed Bayesian market-maker pricing rule, the equilibrium spread is $\mu(1-2\eta)\Delta$, where $\mu$ is the...

arXiv CS 8d ago

A Perturbed q-Tsallis Self-Concordant Barrier for Spectrally Robust Semidefinite Programming

Announce Type: cross Abstract: We introduce and analyse a perturbed $q$-Tsallis barrier for semidefinite programming (SDP), defined as a spectral perturbation of the classical log-det barrier on the cone of positive definite matrices. The barrier introduces eigenvalue-adaptive stiffening through a Tsallis-type matrix-power term controlled by parameters $q>1$ and $\eta\geq0$. Our main theoretical contribution is a sharp characterisation of the differential self-concordance regime of the...

arXiv CS 6d ago

Cenk Uygur and Hasan Piker: the US commentators banned from the UK – podcast

The leftwing American commentator Cenk Uygur talks about the ban on him and his nephew, Hasan Piker, entering the UK this week. With reporting from Kiran Stacey“We’re not allowed to put you on the plane,” said the woman at the terminal. “You can’t board because the British government has withdrawn your ETA.”

The Guardian Politics 6d ago

Robust Predictive Uncertainty and Double Descent in Contaminated Bayesian Random Features

arXiv:2602.19126v2 Announce Type: replace Abstract: We propose a robust Bayesian formulation of random feature (RF) regression that accounts explicitly for prior and likelihood misspecification via Huber-style contamination sets. Starting from the classical equivalence between ridge-regularized RF training and Bayesian inference with Gaussian priors and likelihoods, we replace the single prior and likelihood with $\epsilon$- and $\eta$-contaminated credal sets, respectively, and perform...

arXiv CS 8d ago

Why have two US commentators been banned from entering the UK?

Cenk Uygur and Hasan Piker were supposed to address events at SXSW London before their ETAs were cancelledFree speech activists condemn UK entry ban for Hasan Piker and Cenk UygurCenk Uygur, the host of the Young Turks online political talkshow, and Hasan Piker, who runs his own hours-long stream each day, have been banned from entering the UK by the British home secretary, Shabana Mahmood. They were supposed to address events at SXSW London, a creatives-led festival. Uygur was also planning...

The Guardian Politics 8d ago

Why have two US commentators been banned from entering the UK?

Cenk Uygur and Hasan Piker were supposed to address events at SXSW London before their ETAs were cancelledFree speech activists condemn UK entry ban for Hasan Piker and Cenk UygurCenk Uygur, the host of the Young Turks online political talkshow, and Hasan Piker, who runs his own hours-long stream each day, have been banned from entering the UK by the British home secretary, Shabana Mahmood. They were supposed to address events at SXSW London, a creatives-led festival. Uygur was also planning...

The Guardian UK 8d ago

UK government bans two US political commentators

UK government bans two US political commentators LONDON: Britain's interior ministry on Monday (Jun 1) said it had blocked two US-based politicalcommentators from entering the country. Left-wing Israel critics Cenk Uygur, 56, and his nephew Hasan Piker, 34, had been due to speak at the SXSW London festival this week. "These individuals' Electronic Travel Authorisation (ETA) has been cancelled on the grounds that their presence in the UK may not be conducive to the public good," the ministry...

Channel News Asia 8d ago