Proof The proof can be found in Appendix A.5.

      Properties of LOCATESIGNAL

      In our intuition, we made a claim that if uniformly at random, and i > 16w, then is “roughly uniformly distributed about the circle” and hence not concentrated in any small region. This is clear if β is chosen as a random real number; it is less clear in our setting where β is a random integer in this range. We now prove a lemma that formalizes this claim.

      Lemma 4.6 Let T ⊂ [m] consist of t consecutive integers, and suppose β ∈ T uniformly at random. Then for any i ∈ [n] and set S ⊂ [n] of l consecutive integers,

      Proof Note that any interval of length l can cover at most elements of any arithmetic sequence of common difference i. Then is such a sequence, and there are at most intervals an + S overlapping this sequence. Hence, at most of the β ∈ [m] have βi mod n ∈ S. Hence, .

      Lemma 4.7 Let i ∈ S. Suppose none of E_coll(i), E_off(i), and E_noise(i) hold, and let j = hσ,b(i). Consider any run of LOCATEINNER with . Let f > 0 be a parameter such that

      for C larger than some fixed constant. Then with probability at least ,

      Конец ознакомительного фрагмента.

      Текст предоставлен ООО «ЛитРес».

      Прочитайте эту книгу целиком, купив полную легальную версию на ЛитРес.

      Безопасно оплатить книгу можно банковской картой Visa, MasterCard, Maestro, со счета мобильного телефона, с платежного терминала, в салоне МТС или Связной, через PayPal, WebMoney, Яндекс.Деньги, QIWI Кошелек, бонусными картами или другим удобным Вам способом.

/9j/4SOaRXhpZgAATU0AKgAAAAgABwESAAMAAAABAAEAAAEaAAUAAAABAAAAYgEbAAUAAAABAAAA agEoAAMAAAABAAIAAAExAAIAAAAeAAAAcgEyAAIAAAAUAAAAkIdpAAQAAAABAAAApAAAANAALcbA AAAnEAAtxsAAACcQQWRvYmUgUGhvdG9zaG9wIENTNiAoV2luZG93cykAMjAxODowMjoyNiAxMzoy OTowMwAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAIxqADAAQAAAABAAAK5gAAAAAAAAAGAQMAAwAA AAEABgAAARoABQAAAAEAAAEeARsABQAAAAEAAAEmASgAAwAAAAEAAgAAAgEABAAAAAEAAAEuAgIA BAAAAAEAACJkAAAAAAAAAEgAAAABAAAASAAAAAH/2P/iDFhJQ0NfUFJPRklMRQABAQAADEhMaW5v AhAAAG1udHJSR0IgWFlaIAfOAAIACQAGADEAAGFjc3BNU0ZUAAAAAElFQyBzUkdCAAAAAAAAAAAA AAAAAAD21gABAAAAANMtSFAgIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAEWNwcnQAAAFQAAAAM2Rlc2MAAAGEAAAAbHd0cHQAAAHwAAAAFGJrcHQAAAIEAAAA FHJYWVoAAAIYAAAAFGdYWVoAAAIsAAAAFGJYWVoAAAJAAAAAFGRtbmQAAAJUAAAAcGRtZGQAAALE AAAAiHZ1ZWQAAANMAAAAhnZpZXcAAAPUAAAAJGx1bWkAAAP4AAAAFG1lYXMAAAQMAAAAJHRlY2gA AAQwAAAADHJUUkMAAAQ8AAAIDGdUUkMAAAQ8AAAIDGJUUkMAAAQ8AAAIDHRleHQAAAAAQ29weXJp Z2h0IChjKSAxOTk4IEhld2xldHQtUGFja2FyZCBDb21wYW55AABkZXNjAAAAAAAAABJzUkdCIElF QzYxOTY2LTIuMQAAAAAAAAAAAAAAEnNSR0IgSUVDNjE5NjYtMi4xAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABYWVogAAAAAAAA81EAAQAAAAEWzFhZWiAA AAAAAAAAAAAAAAAAAAAAWFlaIAAAAAAAAG+iAAA49QAAA5BYWVogAAAAAAAAYpkAALeFAAAY2lhZ WiAAAAAAAAAkoAAAD4QAALbPZGVzYwAAAAAAAAAWSUVDIGh0dHA6Ly93d3cuaWVjLmNoAAAAAAAA AAAAAAAWSUVDIGh0dHA6Ly93d3cuaWVjLmNoAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAGRlc2MAAAAAAAAALklFQyA2MTk2Ni0yLjEgRGVmYXVsdCBSR0IgY29s b3VyIHNwYWNlIC0gc1JHQgAAAAAAAAAAAAAALklFQyA2MTk2Ni0yLjEgRGVmYXV

---

Скачать книгу