Peng Xu

activity

20122026

most citedForward and Reverse Entropy Power Inequalities in Convex Geometry

73 citations · 118 across the 17 of their papers we have counts for

collaborators

17 papers

math.CT2026

Stratification of Artin motives over local fields

Peng Xu

Let k be a field of characteristic p>0. We prove that for every p-decomposition group P, the tensor-triangulated category \operatorname{DPerm}(P;k) is stratified and its Balmer spe…

math.CT2026

The Telescope Conjecture for Global Representations and FI-modules

Peng Xu

In this paper, we classify the localizing ideals of the derived category D(U) of global representations over a field k of characteristic zero, for various infinite families U of fi…

math.GM2021★ 1 cited

$δ$ - $r$ -Hyperideals and $ϕ$ - $δ$ - $r$ -Hyperideals of Commutative Krasner Hyperrings

Peng Xu, Melis Bolat, Elif Kaya +3

In this paper, our purpose is to define the expansion of $r$ -hyperideals and extend this concept to $ϕ$ - $δ$ - $r$ -hyperideal. Let $ℜ$ be a commutative Krasner hyperring with nonzer…

math.GM2021★ 1 cited

$r$ -Hyperideals and Generalizations of $r$ -Hyperideals in Krasner Hyperrings

Peng Xu, Melis Bolat, Elif Kaya +3

In this study, we examine some properties of $r$ -hyperideals in the commutative Krasner hyperrings. Some properties of $p r$ -hyperideals are also studied. The relation between prime…

math.RT2019

Mod- $p$ maximal compact inductions do not have irreducible admissible subrepresentations

Peng Xu

Let $p$ be a prime number. We show in this short note that mod- $p$ maximal compact inductions of a $p$ -adic split reductive group do not have irreducible admissible subrepresentati…

math.RT2019

On certain Iwahori--Hecke modules of $G L_{3}$ in characteristic $p$

Peng Xu

In this note, we show that the natural analogue of certain finiteness result of Barthel--Livn $e ˊ$ on $G L_{2}$ fails for $G L_{3}$ . More precisely, within the pro- $p$ -Iwaho…

math.FA2018★ 1 cited

An Exact Upper Bound on the $L^{p}$ Lebesgue Constant and The $\infty$ -Rényi Entropy Power Inequality for Integer Valued Random Variables

Peng Xu, Mokshay Madiman, James Melbourne

In this paper, we proved an exact asymptotically sharp upper bound of the $L^{p}$ Lebesgue Constant (i.e. the $L^{p}$ norm of Dirichlet kernel) for $p \geq 2$ . As an application, we also…

math.RT2018

On the pro- $p$ -Iwahori invariants of supersingular representations of unramified $U (2, 1)$

Peng Xu

Let $G$ be the unramified unitary group $U (2, 1) (E / F)$ over a non-archimedean local field $F$ of odd residue characteristic $p$ . In this paper, for any supersingular representation…

math.RT2017

On certain Iwahori representations of unramified $U (2, 1)$ in characteristic $p$

Peng Xu

Let $F$ be a non-archimedean local field of odd residue characteristic $p$ . Let $G$ be the unramified unitary group $U (2, 1) (E / F)$ , and $K$ be a maximal compact open subgroup of $G…

math.PR2017★ 27 cited

Rogozin's convolution inequality for locally compact groups

Mokshay Madiman, James Melbourne, Peng Xu

General extensions of an inequality due to Rogozin, concerning the essential supremum of a convolution of probability density functions on the real line, are obtained. While a weak…

math.CA2016

The norm of the Fourier transform on compact or discrete abelian groups

Mokshay Madiman, Peng Xu

We calculate the norm of the Fourier operator from $L^{p} (X)$ to $L^{q} (X^)$ when $X$ is an infinite locally compact abelian group that is, furthermore, compact or discrete. This…

math.RT2016

Irreducible $p$ -modular representations of unramified $U (2, 1)$

Ramla Abdellatif, Peng Xu

Let $E / F$ be a unramified quadratic extension of non-archimedean local fields of odd characteristic $p$ , and $G$ be the unramified unitary group $U (2, 1) (E / F)$ . For an irreducible…

cs.RO2016★ 4 cited

A Solution to Time-Varying Markov Decision Processes

Lantao Liu, Gaurav S. Sukhatme

We consider a decision-making problem where the environment varies both in space and time. Such problems arise naturally when considering e.g., the navigation of an underwater robo…

cs.IT2016★ 73 cited

Forward and Reverse Entropy Power Inequalities in Convex Geometry

Mokshay Madiman, James Melbourne, Peng Xu

The entropy power inequality, which plays a fundamental role in information theory and probability, may be seen as an analogue of the Brunn-Minkowski inequality. Motivated by this…

math.RT2014★ 2 cited

On the Jacquet Conjecture on the Local Converse Problem for p-adic GL_n

Moshe Adrian, Baiying Liu, Shaun Stevens +1

Based on previous results of Jiang, Nien and the third author, we prove that any two minimax unitarizable supercuspidals of GL_N that have the same depth and central character admi…

math.NT2013★ 8 cited

A remark on the simple cuspidal representations of GL(n, F)

Peng Xu

Let $F$ be a non-archimedean local field of residue characteristic $p$ , $G$ be the group $G L (n, F)$ . In this note, under the assumption $(n, p) = 1$ , we show a simple cuspidal repres…

math.RT2012★ 1 cited

Hecke modules and supersingular representations of U(2,1)

Karol Koziol, Peng Xu

Let F be a nonarchimedean local field of odd residual characteristic p. We classify finite-dimensional simple right modules for the pro-p-Iwahori-Hecke algebra $\mathcal{H}_C(G,I(1…

Stratification of Artin motives over local fields

The Telescope Conjecture for Global Representations and FI-modules

δ-r-Hyperideals and ϕ-δ-r-Hyperideals of Commutative Krasner Hyperrings

r-Hyperideals and Generalizations of r-Hyperideals in Krasner Hyperrings

Mod-p maximal compact inductions do not have irreducible admissible subrepresentations

On certain Iwahori--Hecke modules of GL3​ in characteristic p

An Exact Upper Bound on the Lp Lebesgue Constant and The ∞-Rényi Entropy Power Inequality for Integer Valued Random Variables

On the pro-p-Iwahori invariants of supersingular representations of unramified U(2,1)

On certain Iwahori representations of unramified U(2,1) in characteristic p

Rogozin's convolution inequality for locally compact groups

The norm of the Fourier transform on compact or discrete abelian groups

Irreducible p-modular representations of unramified U(2,1)

A Solution to Time-Varying Markov Decision Processes

Forward and Reverse Entropy Power Inequalities in Convex Geometry

On the Jacquet Conjecture on the Local Converse Problem for p-adic GL_n

A remark on the simple cuspidal representations of GL(n, F)

Hecke modules and supersingular representations of U(2,1)

$δ$ - $r$ -Hyperideals and $ϕ$ - $δ$ - $r$ -Hyperideals of Commutative Krasner Hyperrings

$r$ -Hyperideals and Generalizations of $r$ -Hyperideals in Krasner Hyperrings

Mod- $p$ maximal compact inductions do not have irreducible admissible subrepresentations

On certain Iwahori--Hecke modules of $G L_{3}$ in characteristic $p$

An Exact Upper Bound on the $L^{p}$ Lebesgue Constant and The $\infty$ -Rényi Entropy Power Inequality for Integer Valued Random Variables

On the pro- $p$ -Iwahori invariants of supersingular representations of unramified $U (2, 1)$

On certain Iwahori representations of unramified $U (2, 1)$ in characteristic $p$

Irreducible $p$ -modular representations of unramified $U (2, 1)$